Senate Republicans are wary of making a historic move to nix the filibuster despite growing pressure from conservatives.

Roughly two weeks after Donald Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE's White House win, GOP lawmakers are already facing calls to overhaul Senate rules and help push through the real estate mogul's agenda.

The calls to go "nuclear" are only likely to intensify next year when Democrats begin to carry out their pledge to fight Trump's agenda on areas where they disagree.

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But Senate Republicans are openly skeptical about making a rules change they believe could come back to bite them, when they are inevitably back in the minority.

Sen. Lamar Alexander Andrew (Lamar) Lamar AlexanderGraham: GOP has votes to confirm Trump's Supreme Court nominee before the election The Hill's Morning Report - Sponsored by Facebook - Washington on edge amid SCOTUS vacancy This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda MORE (R-Tenn.), who led a task force to review potential rule changes, said there isn’t “very much” of an appetite to overhaul the filibuster.

“I think most Republicans understand that the Senate is not an institution to impose the majority's will on the country. It’s the one institution in the country that’s capable of developing consensus,” he said. “The Obama administration found that when you try to cram things down people's throats in a partisan way they don’t last.”

Sen. Orrin Hatch Orrin Grant HatchBottom line Bottom line Senate GOP divided over whether they'd fill Supreme Court vacancy MORE (R-Utah), the chairman of the Finance Committee, argued the filibuster was one of the few tools within the government to protect the rights of the minority.

"If we didn't have the filibuster the minority would be nothing in this country. It would be just like the House where 51 percent vote does everything,” Hatch told a local TV station.

But House conservatives and outside groups are already clamoring for Senate Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellPelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Senate GOP aims to confirm Trump court pick by Oct. 29: report Trump argues full Supreme Court needed to settle potential election disputes MORE (R-Ky.) to use the “nuclear option" and get rid of the 60-vote threshold.

They argue keeping it will allow Democrats to stymie Trump’s agenda after voters gave Republicans control of both the White House and Congress for the first time in roughly a decade.

McConnell is so far staying mum, while playing up the need for bipartisan cooperation in the Senate.

“That’s the way the Senate operates. It’s the only legislative body in the world where the majority is not enough. So we don’t have a hammer lock,” he told local reporters. “You need Democratic cooperation to do most things in the Senate ... and I anticipate it.”

McConnell is widely considered an institutionalist loath to change Senate rules. But even if leadership did support going nuclear, it’s unclear if there’s enough support among GOP senators to carry it out.

In addition to Hatch and Alexander, GOP Sens. Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.), Jeff Flake Jeffrey (Jeff) Lane FlakeJeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style MORE (Ariz.), Thom Tillis Thomas (Thom) Roland TillisThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting OVERNIGHT ENERGY: EPA head questions connection of climate change to natural disasters | Pebble Mine executives eye future expansion in recorded conversations | EPA questions science linking widely used pesticide to brain damage in children Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight MORE (N.C.), Ron Johnson Ronald (Ron) Harold Johnson CIA found Putin 'probably directing' campaign against Biden: report This week: Supreme Court fight over Ginsburg's seat upends Congress's agenda GOP set to release controversial Biden report MORE (Wis.) and Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (S.C.) are signaling they aren’t inclined to overhaul Senate rules, though they'll likely face a mountain of pressure to change their minds.

Republicans are expected to have 52 seats next year and would need a simple majority to overhaul Senate rules. They could lose only two senators if they wanted to gut the filibuster.

Conservative senators, who frequently clash with leadership, could also oppose giving up one of their top tools for slowing down legislation they oppose.

Erick Erickson, a conservative radio host, echoed that argument, calling the filibuster “often the last tool available for conservatives to stop the worst excesses of their own party.”

“If you gut the legislative filibuster, you are stopping conservatives from being able to fight for limited government,” he added in a recent op-ed.

Conn Carroll, a spokesman for Sen. Mike Lee Michael (Mike) Shumway LeeMcConnell shores up GOP support for coronavirus package McConnell tries to unify GOP Davis: The Hall of Shame for GOP senators who remain silent on Donald Trump MORE (R-Utah) said he supports keeping the filibuster for the Supreme Court and legislation.

Keeping the filibuster would similarly give Senate GOP leadership — who kept Trump at arm's length for most of the campaign — a failsafe to kill or water down White House-backed proposals they don’t support.

But they’ll likely face immediate pressure to nix the filibuster if there's a fight over Trump’s Supreme Court pick.

Sen. Charles Schumer Chuck SchumerSenate Democrats introduce legislation to probe politicization of pandemic response Schumer interrupted during live briefing by heckler: 'Stop lying to the people' Jacobin editor: Primarying Schumer would force him to fight Trump's SCOTUS nominee MORE (D-N.Y.), the incoming Senate Minority Leader, is warning that his caucus will block any pick they don’t agree with, urging Trump to tap a “mainstream” nominee.

“If it's out of the mainstream, yes, we're going to fight that nominee tooth and nail,” he told Fox News Sunday.

Trump is expected to move quickly to fill the late Justice Antonin Scalia’s seat, and Trump's list of roughly two dozen potential picks, including Lee, has earned praise from Republicans.

Under current Senate rules they’ll need support from at least eight Democrats to overcome the 60-vote threshold. Democrats went "nuclear" on most administration and judicial nominations in 2013, but maintained that threshold for Supreme Court picks.

Pressed if they would back lowering the threshold for high court nominees, GOP senators said only that they expect Trump's judges to get confirmed.

“I would like to see us honor the agreed upon rules, so we’ll see what Democrats choose to do,” Sen. John Cornyn John CornynThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Liberal super PAC launches ads targeting vulnerable GOP senators over SCOTUS fight Senate GOP faces pivotal moment on pick for Supreme Court MORE (R-Texas) told reporters.

Though top lawmakers — including Minority Leader Harry Reid Harry Mason ReidThe Supreme Court vacancy — yet another congressional food fight Trump seeks to turn around campaign with Supreme Court fight On The Trail: Battle over Ginsburg replacement threatens to break Senate MORE (D-Nev.) — openly floated getting rid of the filibuster for Supreme Court nominations, even Democrats who backed easing the Senate rules signaled they don't support going that far.

“We recognize that the Supreme Court is of profound importance. Its integrity is of profound importance to our nation,” said Sen. Jeff Merkley Jeffrey (Jeff) Alan MerkleyThe Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump, Biden renew push for Latino support Sunday shows - Trump team defends coronavirus response Oregon senator says Trump's blame on 'forest management' for wildfires is 'just a big and devastating lie' MORE (D-Ore.). “We did not want to encourage a president and a majority in the Senate of the same party to reach to extremes that would further damage the integrity of the Supreme Court.”

Ten Democratic senators are also up for reelection in 2018 from states carried by Trump. They will likely face political pressure to buck their party and support his nominees and proposals, which could help Republicans get 60 votes.

Sen. Joe Manchin Joseph (Joe) ManchinThe Hill's Morning Report - Sponsored by Facebook - Trump, GOP allies prepare for SCOTUS nomination this week Trump meets with potential Supreme Court pick Amy Coney Barrett at White House Names to watch as Trump picks Ginsburg replacement on Supreme Court MORE (D-W.Va.) became the first Democratic senator to announce he will back Sen. Jeff Sessions Jefferson (Jeff) Beauregard SessionsGOP set to release controversial Biden report Trump's policies on refugees are as simple as ABCs Ocasio-Cortez, Velázquez call for convention to decide Puerto Rico status MORE (R-Ala.) to be attorney general.

Not every Senate Republican is shutting the door to changing the rules, though no senator has appeared publicly eager to overhaul the filibuster.

Sen. Johnny Isakson Johnny IsaksonLoeffler paints herself as 'more conservative than Attila the Hun' in new campaign ad Georgia GOP Senate candidates cite abortion in pushing Ginsburg replacement Loeffler: Trump 'has every right' to fill Ginsburg vacancy before election MORE (R-Ga.), chairman of the Veterans Affairs Committee, signaled he doesn’t agree with the House-led push to nix the filibuster.

“I was in the House 12 years ago, but I’m on our side now,” he quipped.

But he added that he wouldn’t “pick a fight” over a potential change and would wait to take his cue from McConnell and the GOP leadership team.

Sen. John McCain John Sidney McCainCindy McCain endorses Biden: He's only candidate 'who stands up for our values' Biden says Cindy McCain will endorse him Biden's six best bets in 2016 Trump states MORE (R-Ariz.), chairman of the Armed Services Committee, also declined to predict how the fight over the filibuster would play out, stressing it would require a lot of discussion and depend on multiple “factors.”

“[But] have no doubt it is a major step, just like when Harry Reid ... moved to 51 votes on the judges,” he said. “I was not happy at the time.”