WASHINGTON — A turf war over who should defend President Donald Trump in a Senate impeachment trial is raging behind the scenes in Congress as House Republicans push to join Trump’s legal team — an idea that piques the president’s interest — over the objections of Senate Republicans.

House GOP leaders in recent weeks have advocated for Trump’s most aggressive defenders — Reps. Jim Jordan, R-Ohio, John Ratcliffe, R-Texas, and Douglas Collins, R-Ga. — to cross the Rotunda and help White House counsel Pat Cipollone rebut the charges that the president abused his power and obstructed Congress.

Trump, partial to blunt tactics and top-rated TV performances, loves the idea, according to four administration and congressional officials familiar with his thinking who spoke on the condition of anonymity to talk frankly.

Jordan, for example, is a mainstay champion of Trump's on Fox News, where the president once mused that "he's a warrior for me!"

But Senate Majority Leader Mitch McConnell, R-Ky., and his fellow GOP senators have expressed concerns to Trump that a House-led defense could offend moderates, including Sens. Susan Collins, R-Maine, and Lisa Murkowski, R-Alaska. Trump, they argue, has already won the backing of the GOP base, so he and his team need to focus on ensuring Republican unity on an acquittal.

McConnell has been advising Trump and his legal team not to think of the trial as a “made-for-TV-type House setting,” said one individual familiar with the leader’s thinking, “but rather one where ultimately your audience is senators in the middle on both sides, who are actually listening to the arguments here.”

The individual, like others, was not authorized to speak publicly.

Others in the GOP have publicly suggested House Republicans may lack the right temperament to be persuasive for a Senate constituency that expects a no-nonsense trial.

“One thing I’m not eager to do is re-create the circuslike atmosphere of the House — that’s not what we’re going to do here, if we can avoid it,” said Sen. John Cornyn, R-Texas, a McConnell ally. “So I think it seems obvious to me that if the president picks a team that does not include House members, that we’d be more likely to have the dignified process that the Constitution calls for.”

Senior administration and House GOP officials indicated Wednesday that no final decision had been made on whether House Republicans would be part of the defense team.

"There are a lot of rabbits running around claiming to be the very best bunny, but the president hasn't yet decided which set of fuzzy tails he'll use," said one official, who spoke on the condition of anonymity.

The debate highlights the inherent divide between Trump and his instinctive scorched-earth approach and McConnell’s insistence on a strategy geared toward holding his GOP conference together as well as keeping his majority in November’s elections.

While Trump’s gut reaction has been to push for the most aggressive defense possible, playing to his base, McConnell is operating with a narrow margin of 53 Republicans, several up for reelection in 2020 in swing or Democratic-leaning states.

In recent weeks, the president has floated several ideas for his impeachment trial only to see them rebuffed by McConnell, whom the president has repeatedly deferred to on impeachment.

When Trump wanted Senate Republicans to dismiss the charges against him immediately without a trial, McConnell explained to him that was not possible. When Trump then proposed using the trial to ensure that his 2020 rival Joe Biden and the former vice president’s son Hunter Biden were called as witnesses, it was McConnell who convinced him to back a no-witnesses plan.

More recently, McConnell and several Senate Republicans have pushed back on the idea of House Republicans on the defense team. Senate Judiciary Committee Chairman Lindsey Graham, R-S.C., told Trump that senators — who typically abhor being dictated to by House members — will not take kindly to representatives arguing the president’s case.

"It hasn't been decided, but he's listening to senators," said one person familiar with Graham's conversations with Trump.

All parties agree that Cipollone will take the lead defending the president, alongside his deputies, Pat Philbin and Mike Purpura. Jay Sekulow, Trump's personal attorney who represented him during the special counsel's investigation into Russian interference in the 2016 election, will also weigh in.

But some House Republicans, such as Minority Leader Kevin McCarthy of California and Trump ally Mark Meadows of North Carolina, have argued that Cipollone needs assistance from House members who are deeply familiar with the Democrats’ case against Trump. Jordan and Ratcliffe, for example, both sat through hours of closed-door depositions with witnesses testifying about Ukraine; Collins led the unsuccessful effort in the House Judiciary Committee to stop the articles of impeachment from advancing.

All three men also have legal backgrounds and reputations for being aggressive questioners. Jordan, the ranking Republican on the House Oversight and Reform Committee, offered many of the key talking points rebutting Democratic accusations, some that Trump himself touted on Twitter. Ratcliffe, whom Trump briefly nominated to become director of national intelligence last year, was a former U.S. attorney in Texas.

He withdrew from consideration amid questions about his qualifications and whether he had embellished his résumé.

“Regardless of what other team he has, they should be in there helping because they have so much information,” McCarthy said. Added Rep. Scott Perry, R-Pa., a close ally of Jordan: “He has probably the most in-depth knowledge of any member of the entire proceedings.”

Perhaps most important to Trump is the three House members' flair for the dramatic, which the president often says makes for good TV. The Senate trial will be broadcast on national television, and some House Republicans have privately suggested that Cipollone's approach may be too bookish.

Indeed, those who know Cipollone say he is quiet and careful, often shunning the spotlight. A former U.S. Circuit Court of Appeals clerk who went on to be an assistant to the attorney general before joining private practice, he is not an ebullient showman and, while approachable, can seem rigid at times.

Senate Republicans argue that doesn’t matter — and in fact, it may be preferred. In interviews with six senators Tuesday, all praised Cipollone and said he will be a solid defender of Trump — and may even help convince Democrats such as Sen. Joe Manchin of West Virginia to vote to acquit.

"It's a different calculus than it would be for a public hearing that is ultimately more about public consumption than it is about the members themselves," said the individual familiar with McConnell's thinking. "The concern you would have in venturing down some of those more aggressive roads is that you lose the people who ultimately you're going to need most."

Other Republicans expressed reservations about House members joining the team, even one who was a congressman for six years.

Sen. Kevin Cramer, R-N.D., said his former colleagues “are obviously some talented guys,” but Trump needs “the best defense team he can put together — and not so much a PR team.”

“I just think the House process is very different than the Senate process — the responsibilities and authorities are very different,” he said. “In the House, the audience was the country and the political base of the parties. In the Senate . . . the responsibility of the 100 senators is pretty sobering, and I think the defense would do well to make their case to the 100 jurors.”