Chanute, Kansas (CNN) Republicans need to hold small conservative towns like this one in southeastern Kansas if they have any hope of keeping the House majority next week.

So staffers for the GOP candidate in this House race, Steve Watkins, reacted with delight when during a day of door knocking here, a voter walked out onto her front steps and parroted a Republican attack line bombarding the airwaves.

"Shady Paul Davis!" she blared, a reference to the aggressive attack ads launched by House Speaker Paul Ryan's super PAC, which is berating the Democratic candidate in a multimillion-dollar ad campaign shaping this critical race.

Here in the 2nd Congressional District of Kansas, Republicans are mounting a furious push to save a seat that has been in their party's control for a decade -- one of two seats in this deep-red state that President Donald Trump won by more than 20 points but could flip to the Democrats come Election Day. The GOP gave an opening to Democrats with the retirement of Republican Rep. Lynn Jenkins and nominated a political novice who has faced serious questions about whether he inflated his resume -- all the while facing an experienced Democrat who is raising far more money than his opponent.

But while a victory here could help flip the House to the Democrats -- and help make Minority Leader Nancy Pelosi of California the speaker again -- it also underscores the challenges for a party on the cusp of returning to power. Democrats like Davis are running away from their party's leader -- and may need to continue keeping their distance from their leadership to hold on to their seats in conservative districts.

First, though, Pelosi will have to win the gavel -- without the support of Democrats like Davis.

"There isn't a circumstance in which I'm going to support Pelosi," Davis told CNN in Lawrence, Kansas. "I think Democrats generally are going to have to figure out who's the candidate that can get to 218 votes."

Davis added: "I think there are times where you just need some new blood, and I think that this is the time."

If Pelosi becomes speaker, she will likely preside over a caucus with a diverse set of members, with some pushing for impeaching Trump and others eager to align themselves with the White House. Davis, who preaches bipartisanship, tried to tamp down talk about impeaching the President.

"Well, I'm not going to Washington to impeach the President," Davis said. Asked if he would rule that out no matter what emerges from the Russia investigation, he said: "What I can say is this: I'm not interested in going to Washington to impeach the President. I think impeaching a president is a sad event for our country."

According to a CNN tally, 30 Democrats in races that the party has a good chance of winning have already vowed to oppose Pelosi. That means the margin of a Democratic majority will be critical for her to ascend to the speakership. A tiny majority, of one or two seats, could be problematic. But a bigger majority will allow her to afford defections on the House floor when she'll need 218 votes -- or a majority of members present and voting for a candidate -- to win the speakership.

But not all Pelosi detractors will likely win their races. And she has deep ties to much of the caucus, in no small part to her eye-popping fundraising -- more than $121 million for her party and the Democratic Congressional Campaign Committee -- meaning she stands a good shot at becoming speaker in a Democratic majority. The DCCC used that money to bombard key races with ads as well, including just over $3 million in this race, which has seen more than $12 million worth of ads on both sides -- most of them negative.

And that's what has Republicans like Watkins saying the opposition to Pelosi is a farce.

"He's saying what he thinks he has to say in order to get elected," said Watkins, an Army veteran and first-time candidate, who also worked as a defense contractor in Iraq and Afghanistan. "And Kansas voters aren't being fooled by that."

Questions about the candidates' past

The bigger question is whether the ties to Pelosi will even be a deciding factor in this conservative district.

As they went door-to-door here in Chanute last week, Watkins' aides said Pelosi is a motivating factor for some voters. But, they said, she's not the only issue dominating the race.

"I'd say one out of every four people bring up control of Congress," said Dylan Jones, Watkins' campaign field director. "So if they're saying, 'We need to control Congress and Republicans need to get out and vote,' then those people, one out of four, bring up Pelosi."

Indeed, other issues have dominated attention in this race, including questions about Watkins' resume. It started in the GOP primary, with reports about meetings he purportedly held with local Democratic officials in 2017 as he was weighing a run for the seat.

Davis says Watkins has pulled a bait-and-switch.

"He started the campaign by talking to Democratic leaders," Davis said. "And said when meeting with them he was pro-choice, he was pro-LGBT, he was pro-labor union, told them all the things that they wanted to hear. And then he found out that I was gonna run and then he goes and becomes a Republican and now he has taken the opposite position on all of those issues."

Watkins calls that story "fake news," saying he is running now because "I had to look for other ways to serve" after being injured while working as a defense contractor in war zones.

"Oh, not at all," Watkins said when asked about meetings he reportedly took with Democrats. "Not at all. No, that was fake news propagated by my opponents who were running behind in the polls. That was absolutely not true. I would never entertain running as a Democrat."

He emerged from a crowded primary, he said, partly because of his outsider image.

"We knocked on 1,000 doors a day not to persuade but to listen," Watkins said about this sparsely populated district. "And what we heard was that people were really still attracted to an outsider."

While Davis said he voted for Hillary Clinton in 2016, Watkins said he didn't vote at all.

"I didn't vote in 2016. Regretfully, it was a big mistake of mine," Watkins said. "My focus was elsewhere."

But other issues about Watkins' career have taken attention in the race. He had told voters that he started and grew a defense contracting company from scratch. Then the Kansas City Star reported , based on interviews with company officials and records, the company existed before he joined as a consultant.

Watkins told CNN he wasn't misleading voters.

"See, I didn't own the company," Watkins said. "But I helped start and grow it operationally. And that's where they're thinking that they're fashioning me as the liar. That's simply not true."

Still other embarrassing stories have since come out, including one from The Associated Press calling into question a 2015 expedition he took on Mount Everest when a major earthquake occurred in Nepal . Watkins' campaign website quoted an individual who said he showed "heroic leadership amid the chaos." But that man, Guy Cotter, told the AP that he never made those remarks and claimed there was nothing they could have really done to help in the deadly situation.

Asked about the episode, Watkins said he recalled Cotter making those remarks to him. But he said he removed the testimonial once concerns were raised. Nevertheless, he says, "Nothing that happened or didn't happen was even being contested."

"What happened was that there was a 7.8 magnitude earthquake," Watkins said. "We found ourselves -- I was at 19,000 feet. We lived. There were several other fatalities. I exchanged compliments with another climber who doesn't remember the nature of that compliment being the same as I quoted. I said sorry, I took it down."

Davis said it shows Watkins' lack of disregard for the truth.

"This is just a pattern that we have seen over and over from Steve Watkins," Davis said. "I don't think he can be trusted."

But Davis, too, has endured sharp attacks about his past. Ryan's super PAC, the Congressional Leadership Fund, has dropped $3.7 million on the airwaves, with many attacks calling Davis "shady" over an embarrassing incident from 1998. At the time, Davis was at a strip club getting a lap-dance from a topless woman when the police entered the venue on a raid for drugs.

Davis, who was 26 and not married at the time, was not charged with any crime, but a police report said it found him in a "somewhat compromising position" with the dancer. He says he was in the club only because his boss, one of his legal clients, was the owner of the facility and took him to the venue.

The controversy flared up in the heat of Davis' unsuccessful run for governor in 2014 against Republican Sam Brownback. And it hasn't stopped since.

"Well, I was in the wrong place at the wrong time," Davis told CNN when asked to recount the 1998 incident. "And, you know, it's one incident and I think it's old news to most Kansans. They ran this attack back in 2014 when I ran for governor and I don't think it was effective then, and I don't really think it's effective now."

Asked about the incident, Watkins said: "Well, you know, if I was in his position, I wouldn't have found myself in a strip club in the '90s."

But he also distanced himself from the aggressive GOP attack ads, a sign that voters may be growing weary at this stage of the hard-fought campaign.

"I don't support -- they're not a product of me," Watkins said about the GOP ads, stopping short of saying they should be taken down. "I've run an aspirational campaign."