Senate Republicans realize they need to push back more aggressively on the fast-moving impeachment inquiry in the House, but they have yet to display a unified strategy.

The disunity comes as public opinion polls show growing support for impeachment proceedings, giving more momentum to congressional Democrats almost three weeks after Speaker Nancy Pelosi Nancy PelosiDemocratic senator to party: 'A little message discipline wouldn't kill us' Overnight Health Care: New wave of COVID-19 cases builds in US | Florida to lift all coronavirus restrictions on restaurants, bars | Trump stirs questions with 0 drug coupon plan Overnight Defense: Appeals court revives House lawsuit against military funding for border wall | Dems push for limits on transferring military gear to police | Lawmakers ask for IG probe into Pentagon's use of COVID-19 funds MORE (D-Calif.) announced the inquiry.

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Senate Judiciary Committee Chairman Lindsey Graham Lindsey Olin GrahamLincoln Project mocks Lindsey Graham's fundraising lag with Sarah McLachlan-themed video The Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election Trump dumbfounds GOP with latest unforced error MORE (R-S.C.) is spearheading the GOP counteroffensive and plans to call President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE’s personal lawyer, Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE, before his panel to testify about former Vice President Joe Biden Joe BidenFormer Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick Bloomberg rolls out M ad buy to boost Biden in Florida MORE and Ukrainian corruption.

But Senate GOP aides warn the risky move could backfire on Republicans.

“I think bringing Rudy Giuliani to the Senate Judiciary Committee is probably a mistake,” said a Senate Republican aide, who requested anonymity to discuss party strategy. “He’s not the stable lawyer that he once was. He’s become Trumpian in saying whatever sounds good at the moment. It’s one thing when you’re doing that on TV, it’s another when you’re under oath to a congressional committee.”

The aide, however, said there’s pressure on Graham to get more aggressive in response to the escalating tactics of House Democrats.

“If the House isn’t going to follow the norms of impeachment and do a vote and do legitimate live hearings then I think Graham is going to be more inclined to do some stunts,” the aide said.

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Graham initially said he did not want to delve into the allegations being pushed by Giuliani, who claims that efforts to interfere in the 2016 election likely originated in Ukraine. He is also calling for an investigation into unsubstantiated allegations that Biden interfered in Ukrainian anti-corruption efforts.

Graham told reporters before the two-week October recess that he didn’t want to unleash a storm of partisan bickering by launching a Ukraine probe.

“I don’t want to turn the Senate into a circus,” he said. “We’re not going to do anything because we don’t have any jurisdiction. I have no interest in opening up that front. I don’t want to blow up the Senate.”

But Graham, who has been in contact with Giuliani, abruptly shifted gears this past week, announcing he will now have Trump’s personal lawyer testify.

“It’s very helpful because at the right time it will give me the opportunity to show all my evidence as if I were prosecuting a case. If they don’t think they I have evidence, they don’t me,” Giuliani told The Hill in an interview Thursday.

Giuliani called Graham “a good friend of mine,” saying he has talked to the South Carolina Republican, considered one of Trump’s strongest Senate allies, about efforts to delve into the Ukraine controversy.

Senate Democrats, meanwhile, are itching to pounce on Giuliani if he comes up to Capitol Hill. Senate Minority Leader Charles Schumer Chuck SchumerPelosi slams Trump executive order on pre-existing conditions: It 'isn't worth the paper it's signed on' 3 reasons why Biden is misreading the politics of court packing Cruz blocks amended resolution honoring Ginsburg over language about her dying wish MORE (D-N.Y.) has demanded he testify under oath.

Democrats could barrage Giuliani with a range of questions about Trump’s involvement in efforts to push Ukraine to investigate Biden, and give the three Democrats on the panel running for president — Sens. Amy Klobuchar Amy Klobuchar3 reasons why Biden is misreading the politics of court packing Social media platforms put muscle into National Voter Registration Day Battle lines drawn on precedent in Supreme Court fight MORE (Minn.), Cory Booker Cory Anthony BookerThe movement to reform animal agriculture has reached a tipping point Watchdog confirms State Dept. canceled award for journalist who criticized Trump 3 reasons why Biden is misreading the politics of court packing MORE (N.J.) and Kamala Harris Kamala HarrisTexas Democratic official urges Biden to visit state: 'I thought he had his own plane' The Hill's Campaign Report: Biden on Trump: 'He'll leave' l GOP laywers brush off Trump's election remarks l Obama's endorsements A game theorist's advice to President Trump on filling the Supreme Court seat MORE (Calif.) — a national platform to go on the attack.

Giuliani told The Hill that he would expect to testify under oath but hasn’t yet decided whether he’ll accept Graham’s invitation.

If he doesn’t testify, it would present Graham with a serious dilemma of whether to move ahead without a star witness.

Giuliani told The Hill that he’s working on lining up alternative witnesses.

“I began it and I have the best overview of it,” he said of his investigation into Ukrainian corruption and possible ties to Biden. “Some of these Ukrainians have a lot more information than I have. So I’m trying to get them to come over here to get interviewed.”

Democrats would undoubtedly challenge the credibility of Giuliani’s witnesses, particularly in the wake of federal charges filed against two of his associates, Lev Parnas and Igor Fruman, who helped dig up information on Ukrainian corruption and potential links to Biden.

Ukrainian-born Parnas and Fruman, who was born in Belarus, were arrested Wednesday night at Dulles International Airport with one-way tickets out of the country. Both men are U.S. citizens.

Giuliani suggested that Graham has also changed his mind on inviting Biden and his son Hunter to testify.

But the Senate Republican aide predicted that’s unlikely.

“I don’t think that Biden would be called. I think that’s probably Giuliani more than Graham,” the aide said.

Launching a Senate investigation into Ukrainian corruption and the Bidens could put vulnerable Republicans in a tough spot heading into 2020.

Sen. Cory Gardner Cory Scott GardnerBreaking the Chinese space addiction Trump dumbfounds GOP with latest unforced error Billionaire who donated to Trump in 2016 donates to Biden MORE (R-Colo.), a top Democratic target next year, repeatedly declined to say Thursday if it was appropriate for Trump to ask a foreign leader to investigate Biden.

GOP Sens. Joni Ernst Joni Kay ErnstOn The Trail: Making sense of this week's polling tsunami Tillis appears to reinforce question about COVID-19 death toll The power of incumbency: How Trump is using the Oval Office to win reelection MORE (Iowa) and Martha McSally Martha Elizabeth McSallyOn The Trail: Making sense of this week's polling tsunami The Hill's Campaign Report: Presidential polls tighten weeks out from Election Day Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (Ariz.), two other incumbents up for reelection next year, also stopped short of rendering a judgment.

Ernst said she didn’t have enough information and McSally just urged Congress to treat the impeachment inquiry in a “serious and solemn manner.”

A second Senate Republican aide said GOP leaders initially wanted to steer clear of the politics of impeachment and paint it as a frivolous, partisan exercise by House Democrats that would interfere with passing regular legislation.

But the thinking has changed in light of new polls showing Democrats are making strides in the court of public opinion, with a growing number of Americans now saying Trump should be impeaching.

“What Graham is thinking is the House is producing all this news and information and it’s all against the president, and when it’s not, they don’t release it,” said the GOP aide.

“I think there’s a desire within the conference to go on offense and that’s what this is,” the aide added.

A Fox News poll released Wednesday showed that a record 51 percent of voters want to see Trump impeached and removed from office.

A survey by PBS NewsHour, NPR and Marist published Thursday found that 52 percent of Americans and 54 percent of independents support the impeachment inquiry.

Graham said he plans to circulate a letter among fellow Senate Republicans informing Pelosi that a majority of the Senate GOP conference believes Trump’s phone call with Ukrainian President Volodymyr Zelensky was not an impeachable offense.

Other Senate Republicans have also stepped up their attacks on Pelosi in recent days.

Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellDemocratic senator to party: 'A little message discipline wouldn't kill us' House to vote on resolution affirming peaceful transition of power Republican lawyers brush off Trump's election comments MORE (R-Ky.) on Tuesday blasted House Democrats for launching the impeachment inquiry.

“Overturning the results of an American election requires the highest level of fairness and due process, as it strikes at the core of our democratic process,” he tweeted. “So far, the House has fallen far short by failing to follow the same basic procedures that it has followed for every other President in our history.”

The emerging consensus among Republicans is that the best way to respond to any articles of impeachment passed by the House is to dismiss them as quickly as possible in the Senate, likely without a trial.

Giuliani told The Hill that a Senate trial would have negative repercussions on the country.

“It would probably be dismissed immediately,” he said, adding it would be “horrible” if impeachment articles passed the House and resulted in a Senate trial.