Originally Published: 16 JUL 21 15:28 ET

Updated: 19 JUL 21 11:26 ET

By Manu Raju and Alex Rogers, CNN

(CNN) -- Former President Donald Trump made his return to campaign politics last month by trekking to northern Ohio to take revenge on one of the 10 Republicans who voted to impeach him: Rep. Anthony Gonzalez.

But new campaign finance filings released this week show that Gonzalez narrowly outraised his Trump-supported primary foe in the last quarter, while boasting a war chest nearly three times the size of his opponent.

The 10 House Republicans who voted to impeach Trump for inciting the January 6 insurrection are fully aware that the former President and his acolytes are determined to kick them out of their seats from South Carolina to California. Between April and June, nine out of 10 raised more money than their primary foes, and all 10 have more cash on hand than them, pitting the enduring strength of Trump's sway against the power of incumbents who have the ability to raise piles of cash in Washington and from around the country. One Republican — New York Rep. John Katko — does not even have a primary challenger yet, although Trump has pledged to find one.

"Many times I couldn't care less what the former President says about me or says period -- other than the more dangerous elements of his speeches obviously," Gonzalez told CNN.

While Trump remains the dominant force in the GOP, what is less clear is how powerful his endorsement will turn out to be next year -- and whether the former President will actually invest the time, energy and money to defeat those incumbents.

The National Republican Congressional Committee, which is the House GOP's main campaign arm, is staying out of the primaries -- saying it's the group's policy not to engage in intraparty conflicts -- leaving the candidates to fend for themselves.

Some Republicans facing the Trump onslaught say they're perfectly fine with that.

"I don't want any help [from the NRCC]," said Wyoming Rep. Liz Cheney, a vocal Trump critic who raised nearly $1.9 million in the second quarter, beating her closest challenger by more than $1.6 million.

The GOP lawmakers are facing off largely against primary opponents who are perpetuating Trump's lie that the election was stolen from him, a litmus test of sorts for candidates eager to win the former President's endorsement.

Joe Kent, a retired US Army Special Forces officer and Gold Star husband, who is taking on Washington Rep. Jaime Herrera Beutler with the support of billionaire venture capitalist Peter Thiel, told CNN: "I think Trump won, but I want to prove it."

House GOP campaign boss plans to stay out of primaries

The two biggest fundraisers of the 10 who voted to impeach Trump have also been the most vocal against the former President: Cheney and Illinois Rep. Adam Kinzinger.

Kinzinger vastly outraised the competition, raking in $806,475 between April and June. He now boasts a campaign war chest of over $3 million, more than 20 times his GOP challenger Catalina Lauf's cash on hand.

The GOP members contend they are not concerned about the prospects of a tough primary.

"I'm looking forward to it," said Cheney when asked about her primary against state legislators Chuck Gray and Anthony Bouchard, businessman Darin Smith and others. "It's going to be a great race."

Minnesota Rep. Tom Emmer, the NRCC chairman, told CNN that House members and other political committees can get involved in House races, but that his organization would not interfere in Republican primaries, even for members in swing districts like California Rep. David Valadao, who voted to impeach Trump.

"We don't want the heavy hand of Washington stepping into the debate, the discussion, that constituents in a certain district are having over the representation," Emmer said. "That being said, I absolutely want to see them win."

In Ohio, Trump endorsed Max Miller, a 32 year-old former Marine Corps Reservist and Trump campaign staffer, to take Gonzalez's seat in 2022, and campaigned for Miller in June at his first rally since leaving the White House. New campaign filings show that Miller raised over $443,000 in the second quarter of the year, an impressive figure for a first-time candidate boosted, no doubt, by Trump.

But Gonzalez raised even more -- over $602,000 -- and his campaign has $1.5 million on hand -- nearly three times the size of Miller's war chest, as he shielded himself from the fallout.

When asked if it would be helpful if the NRCC backed his campaign, Gonzalez said, "Sure," but didn't seem to be counting on any help. "I've been around long enough to know you've got to take care of your own business," he added.

"I welcome their support but I'm not waiting for some silver bullet from the outside."

McCarthy helps raise money for some Republican Trump critics

Half of the 10 House Republicans who voted to impeach Trump -- Valadao, Beutler, Katko, and Michigan Reps. Fred Upton and Peter Meijer -- have a joint fundraising committee with House GOP Leader Kevin McCarthy and his leadership PAC, which has raised roughly $100,000 for each of the five campaigns in the first half of the year. The joint fundraising committee -- known as Take Back the House 2022 -- has not raised money for the other five: Cheney, Kinzinger, Gonzalez, Washington Rep. Dan Newhouse and South Carolina Rep. Tom Rice.

When asked if the House GOP leadership has helped his campaign, Valadao said, "They've all been very, very supportive."

Challengers typically have a harder time raising money against incumbents, who already have established a connection with voters, donors and powerful allies like McCarthy. Some of the pro-Trump challengers will be a long-shot unless Trump comes to their aid.

"It's difficult for a Republican challenger in a primary when you have a sitting Republican to raise money," Chris Mathys, a Republican candidate running against Valadao, told CNN. "At the end of the day, we're looking for support from the voters in the district. And they are extremely upset with Mr. Valadao's betrayal of his oath of office."

Mathys, who said he believes that Trump won the 2020 election, raised $12,300 in the second quarter, and gave his campaign a $100,000 loan. Valadao raised over $482,000 and has on hand nearly $820,000 -- quadruple Mathys' figure.

Asked if he believes his vote to impeach Trump will hurt him in the primary, Valadeo told CNN: "It's hard to say. It really is. But we'll find out."

Pro-Trump challengers like Mathys believe that they will get grassroot support despite their meager fundraising hauls. But some challengers have actually raised the money to wage a credible campaign even without Trump's endorsement.

In the second quarter, South Carolina GOP House candidate Graham Allen raised over $501,000 including a $92,000 loan he made to his campaign, while Rice raised about $327,000. (Rice's campaign, however, has more than a million dollars more on hand than Allen's.)

In Washington state, Kent became more politically active after his wife, Navy cryptologist Shannon Kent, was killed in 2019 conducting Special Operations against ISIS in Syria. Kent then decided to run for Congress after Beutler's impeachment vote, and has made "election integrity" one of his top campaign issues even though there is no evidence of widespread voter fraud in the 2020 election. After raising over $366,000 in the second quarter, Kent has $512,150 on hand -- about half of Beutler's cash.

"I want a full forensic audit of any place (where) there was widespread discrepancies," Kent said of the 2020 elections.

Yet most of the Republicans facing a tough primary challenge are simply shrugging it off.

"I can't control what he does, and he can't control what I do," Rice said of Trump.

CORRECTION: An earlier version of this story misstated the number of impeachment-supporting House Republicans who had outraised their GOP primary opponents in the second quarter. It was nine out of 10.