"There wasn’t any pushback to it," she said. "There’s wasn’t anyone saying: oh wait a minute. That didn’t occur."

McConnell’s advice comes one day after the Electoral College officially voted for Joe Biden as the president-elect. The Kentucky Republican acknowledged for the first time that Biden will be the next president in his floor remarks Tuesday.

Several House Republicans, led by hard-line conservative Rep. Mo Brooks (R-Ala.), are still planning to challenge the election results on Jan. 6, the date Congress will officially certify them. If a Republican senator joins the long-shot effort, however, it will force both chambers to take a vote on the election. But they have yet to get official buy-in from any GOP senators, though Sen. Rand Paul (R-Ky.) hasn't ruled it out.

Brooks, in response to McConnell cautioning the GOP against objecting to the election results, tweeted that he hopes it’s “fake news.”

“I find it unfathomable that anyone would acquiesce to election theft and voter fraud because they lack the courage to take a difficult vote on the House or Senate floor,” Brooks said in a phone interview. “Last time I checked, that’s why we were elected to Congress.”

Brooks met briefly last week with several GOP senators to discuss his effort, but declined to say whether anyone is seriously considering the idea. Conservatives, however, have been eyeing Sen.-elect Tommy Tuberville — another Alabama Republican and Trump supporter — as someone who may get on board. And Senate Republicans are unsure where he stands; Tuberville was not a part of Tuesday’s conference call.

McConnell’s warning underscores how the last-ditch bid to overturn the election is putting the GOP in a bind. On the one hand, Republicans are facing pressure from Trump and his allies to support his attempt to remain in power. And party leaders want to keep the base energized ahead of a pair of critical Georgia runoff races on Jan. 5. that will determine control of the Senate.

But at the same time, McConnell — who is defending a tough Senate map in 2022 — needs to protect his members from taking a tough vote. If the Senate is forced to deliberate the election results, most GOP senators would be going on the record against a president who values fealty above all else. And it would be none other than Vice President Mike Pence presiding over the floor debate — a potentially awkward scenario as his boss continues to deny the reality of the election he lost.

McConnell on Tuesday’s call cited a 2005 objection from former Sen. Barbara Boxer (D-Calif.) after President George W. Bush’s reelection, which delayed the process by a few hours, according to several sources. The Kentucky Republican warned that he hoped no one, particularly in the class of 2022, thought that was a good idea.

Meanwhile, House Minority Leader Kevin McCarthy — a top Trump ally who has yet to recognize Biden as the president-elect — has dodged questions from reporters about whether he supports Brooks' gambit. But McCarthy did say during a recent appearance on Fox Business Network that the courts are the proper venue to dispute election results.

“The president is right to go to the courts, have his legal challenges heard,” McCarthy added. “And he said he still has more opportunity to do that, so we'll wade through and see what happens.”

On Friday, the Supreme Court rejected a longshot bid by Texas and other Republican-led states to overturn the election results. McCarthy had joined that effort.

Trump has yet to show any sign that he will concede. Instead, the president on Tuesday continued to reiterate false claims of voter fraud on Twitter.

The president is also publicly and privately leaning on his Hill allies to launch a last-ditch effort to reverse the election in Congress. He has praised Brooks on Twitter and retweeted a Breitbart News article Tuesday in which Brooks vows to continue fighting the Electoral College results in Congress.

Yet even if a GOP senator gets on board, the effort is doomed to fail, given the makeup of the Democratic-led House and the increasing number of Senate Republicans who have recognized Biden as the president-elect. Still, it could become yet another Trump loyalty test in the GOP.

In January 2017, a handful of House Democrats took this precise procedural step before their efforts flamed out during a joint session of Congress presided over by Biden, then the outgoing vice president.

“It is over,” Biden said at the time, gaveling down Democrats as Republicans cheered.

Jake Sherman and Burgess Everett contributed to this report.