FILE - In this Aug. 10, 2019, file photo, then Democratic presidential candidate former Colorado Gov. John Hickenlooper speaks at the Presidential Gun Sense Forum, in Des Moines, Iowa. Hickenlooper was supposed to be Democrats' worry-free solution to the Colorado Senate race, but he's stumbled badly in the weeks leading up to the party's June 30 primary. (AP Photo/Charlie Neibergall, File)
CNN  — 

Last week’s down-ballot primary action in New York still isn’t settled, but it’s time for three more states – Colorado, Utah and Oklahoma – to host primaries Tuesday, and there’s at least one contest in each state that could help shape the balance of power in Congress next year.

The Democratic Senate primary in Colorado has garnered the most national attention. Democrats need to flip three seats (if they win the White House) or four seats (if they don’t) to control the Senate next year. Colorado, which voted for Hillary Clinton by 9 points in 2016, may be their biggest target. The national party has already settled on its candidate to take on GOP Sen. Cory Gardner, but on Tuesday, voters will have their say.

Whereas Democrats are on offense in the Senate, they’re mostly playing defense in the House, trying to hold onto their historic gains from the 2018 midterms. Democrats flipped seats that President Donald Trump carried in 2016, including one in Oklahoma and Utah, and now Republicans want them back.

Also in Utah, former Gov. Jon Huntsman, who’s since run for president and served as Trump’s ambassador to Russia, is trying to get his old job back.

Here’s what to watch on Tuesday:

Will the national Democratic party’s pick be the nominee in the Colorado Senate race?

Sen. Cory Gardner, Colorado’s first-term Republican senator, is one of the most vulnerable incumbents facing reelection in the fall. Tuesday’s primary will decide who’s taking him on and what that November match-up could look like in a state that’s shifted blue.

Former two-term Gov. John Hickenlooper, who ran a short-lived campaign for the 2020 Democratic presidential nomination, is the national party’s pick to take on Gardner, one of two Republicans facing reelection in a state Clinton carried in 2016.

But Hickenlooper, long seen as the Democratic frontrunner, faces competition from his left, and after a series of negative headlines in June, Tuesday’s primary will be seen as a test of whether voters pass over the national party’s pick.

Andrew Romanoff is no stranger to campaigns. The former state House speaker unsuccessfully challenged newly-appointed Sen. Michael Bennet in a 2010 Democratic primary. Four years later, he lost a bid for a Denver-area House seat. Now he’s running for the Senate nod, campaigning on “Medicare for All” and the Green New Deal.

Hickenlooper has statewide name recognition, large campaign coffers and the powerful backing of outside groups spending on his behalf. But missteps on his part may have, at least temporarily, shaken his apparent advantage. In a sign that his allies were getting nervous, a new pro-Hickenlooper super PAC started spending more than $1 million attacking Romanoff last week. That’s given Romanoff fodder to call Hickenlooper’s pledge to get dark money out of politics hypocritical.

Hickenlooper has recently tried to clean up past remarks. He said he “tripped” when he said that “Black Lives Matter” means that “every life matters” – a description activists say discounts the systemic discrimination against Black people. He apologized for resurfaced comments he made in 2014 comparing politicians to slaves being whipped to row “an ancient slave ship.”

But it’s Hickenlooper’s ethics violations that Republicans have been hammering him on. The state’s Independent Ethics Commission first found him in contempt for defying a subpoena to show up for a remote hearing. Then after he did testify virtually, the commission fined him earlier this month for twice violating the rule against accepting gifts when he was governor, even though it dismissed most of the allegations against him.

Romanoff has piled on to the GOP attacks, running an ad that says, “We can’t take this kind of risk if we’re going to beat Cory Gardner” and calling for a “fresh, progressive voice in the Senate.” But national progressive icons like Massachusetts Sen. Elizabeth Warren and Georgia 2018 Democratic Lt. Gov. nominee Stacey Abrams, as well as New Jersey Sen. Cory Booker have all recently endorsed Hickenlooper.

And Hickenlooper’s allies have been attacking Romanoff on his support for 2006 immigration bills, trying to make the case that he may not always have been as progressive as he says he is now.

“Whatever momentum existed for Romanoff got stalled about a week ago, 10 days ago,” Colorado-based Democratic strategist Rick Ridder, who’s not working for either candidate, said on Monday.

Hickenlooper had spent about $6.7 million by the end of the pre-primary reporting period on June 10 – more than three times what Romanoff had spent – and that’s independent of the millions of dollars national Democratic groups have spent for him. Hickenlooper ended the period with nearly $6 million in the bank, compared to Romanoff’s $792,000, according to filings with the Federal Election Commission.

If Hickenlooper wins the nomination, he’ll be the second failed 2020 presidential candidate who said he wanted no part of the Senate but is now trying to flip a red Senate seat. Both he and Montana Gov. Steve Bullock faced pressure from the national party to use their statewide name recognition to take on Republican incumbents. Gardner has already used that original lack of enthusiasm for the Senate against Hickenlooper in an ad where he says, “To do this job, you probably need to want this job.”

The general election is rated Tilt Democrat by Inside Elections with Nathan L. Gonzales, who is a CNN contributor.

It was the 2018 upset Republicans didn’t see coming. Who will try to avenge the loss this year?

Democrat Kendra Horn’s victory over then-Rep. Steve Russell, a two-term Republican, was perhaps the biggest surprise of the 2018 midterms. The race for Oklahoma’s 5th District, which Trump carried by more than 13 points, hadn’t been on many people’s radar two years ago. Horn became the first Democrat in decades to represent the Oklahoma City area, which now includes younger and well-educated suburbs that Democrats think will benefit them this fall. Inside Elections rates the general election a Toss-up.

Horn barely won – she defeated Russell by 1 point – and nine Republicans are competing on Tuesday to try to take her on. If no one gets a majority of the vote, the top-two finishers will advance to a runoff on August 25.

Among the most competitive candidates are two women, which is in itself noteworthy in a GOP primary, where women have long faced difficult odds but are seeing more success this year. State Sen. Stephanie Bice had raised more than a million dollars by the end of the pre-primary reporting period on June 10. Businesswoman Terry Neese loaned her campaign $450,000 and had raised about $532,000.

The Club for Growth hasn’t endorsed in the race, but its super PAC has been attacking Bice in TV ads in recent weeks. It tried to tie her to Harvey Weinstein because she voted to expand a tax incentive for the film industry to come to Oklahoma and it questioned her support for Trump because in 2016 she backed Carly Fiorina, who recently said she’d vote for Biden in 2020. (The Club, which now backs the President, initially opposed Trump in the 2016 primary.)

“There are too few Republican women in Washington right now,” Bice said in a Facebook live message to her supporters on Saturday. “Sexism in attacks from groups like this is one of the biggest reasons why.”

Club for Growth Action President David McIntosh responded by attacking her support for what he called “the largest tax increase in Oklahoma state history” and “her support for never-Trumper Carly Fiorina.”

“There are other women and men in this race who don’t support higher taxes or using taxpayer money to support Hollywood,” McIntosh said in a statement.

Republicans choose nominee for another possible House pick-up

Republicans are selecting their nominee for another seat that Democrats flipped in 2018, when Ben McAdams narrowly defeated Mia Love. Unlike Oklahoma’s 5th District, Utah’s 4th District has a more recent history of being in Democratic hands. Inside Elections rates the race Tilt Democratic.

Still, Trump carried the district by nearly 7 points, and it’s a top target for the GOP this fall. The party didn’t have an obvious frontrunner candidate, though, after state Sen. Dan Hemmert dropped out of the race in December.

Four candidates are running. Former NFL player Burgess Owens, a Fox News commentator, has raised the most money as of the pre-primary report, followed by state Rep. Kim Coleman. Both are on the lowest level of the National Republican Congressional Committee’s “Young Guns” list for competitive candidates.

Will Huntsman get his old job back in Utah?

Four Republicans are also vying for the nomination to succeed outgoing Gov. Gary Herbert in Utah, a red state that votes by mail.

Among those candidates is Jon Huntsman, who was twice elected governor before stepping down in 2009 to serve as then-President Barack Obama’s ambassador to China. Huntsman ran unsuccessfully for the GOP nomination for president in 2012. He submitted his resignation as Trump’s ambassador to Russia last August, returning to the Beehive State to run for office.

But Huntsman, who, along with his wife, has tested positive for coronavirus this month, is in a tight race.

A Suffolk University/Salt Lake Tribune poll from earlier this month showed Lt. Gov. Spencer Cox leading with 32% among likely GOP primary voters, followed by Huntsman at 30% – a difference that was within the margin of error. Former state House Speaker Greg Hughes and former Utah Republican Party Chairman Thomas Wright trailed.

This story has been updated to include additional developments Tuesday.

CNN’s Fredreka Schouten contributed to this story.