(CNN) House conservatives are undeterred by Senate Majority Leader Mitch McConnell's push to squelch their efforts to contest the presidential election results when a joint session of Congress meets in January to formally count the electoral votes that made Joe Biden's win official.
"I know there is zero chance of succeeding if you are a member of the surrender caucus," said Rep. Mo Brooks, a Republican of Alabama who is a leader of the effort. "There is some chance of succeeding if you fight."
The comments are the latest sign that many House Republicans are not ready to accept the results of the election as leading conservatives continue to echo President Donald Trump's false voter fraud claims that have yet to be proven in court -- and House GOP leaders remain silent on acknowledging that Biden is the President-elect.
Indeed, even as McConnell ultimately congratulated Biden on Tuesday and referred to him as the "President-elect" for the first time, House Minority Leader Kevin McCarthy was silent when asked if he'd acknowledge Biden's win, while his No. 2, Steve Scalise, has yet to publicly accept the results himself.
The conservative effort to attempt to overturn states' election results is doomed to fail. But it could put Republicans in a bind.
Privately, McConnell -- along with his top deputies, GOP Sens. John Thune of South Dakota and Roy Blunt of Missouri -- urged GOP senators on a Tuesday call not to join a House effort to object to the results on January 6 since doing so would ultimately force senators to cast a vote on the merits of the objection. GOP leaders fear they would be forced to choose between Trump and the will of the voters -- and are eager not to be put in that position.
"I think there's going to be an objection," Rep. Jim Jordan, an Ohio Republican, said Wednesday. "Whether there'll be a senator to support that or not, I don't know."
Jordan added: "What's wrong with having a debate on the floor of the House and on the floor of the Senate about an election that more than a third of the electorate thinks was stolen?"
While it is not unusual for a losing candidate's most fervent supporters to take their case to the House floor -- something that occurred after the 2016, 2004 and 2000 presidential races, Trump's tactics have unnerved many officials in both parties. He has mounted a weeks-long campaign making one baseless claim after another, has continually lied about the election results, and refuses to concede even when court after court -- including the Supreme Court -- has rejected Republican lawsuits to overturn the results.
It's not clear if any Senate Republicans will join their House colleagues to lodge an objection that would spark a formal debate and ultimately a vote, though several have entertained Trump's false claims of widespread voter fraud. Sen. Ron Johnson of Wisconsin, who held a hearing on Wednesday questioning the handling of the elections, indicated he would not join the House effort.
But several other senators -- Josh Hawley of Missouri, Rand Paul of Kentucky and Kelly Loeffler of Georgia -- have not ruled it out.
"I haven't thought about it or made any plans to do anything," Paul said Wednesday when asked if he would object on January 6. Asked about McConnell's request that GOP senators refrain from that, Paul said: "I wasn't part of that phone call."
A number of Republican House members refused on Wednesday to acknowledge Biden's win.
"The President has some legal options," said Rep. Buddy Carter of Georgia when asked if he considers Biden the President-elect. Rep. Joe Wilson of South Carolina added: "I still think it's premature until all legal disputes are settled," declining to recognize Biden's win.
Brooks, the GOP member leading the effort, is planning to send a letter to McConnell, House Speaker Nancy Pelosi, as well as committee leaders, to ask them to hold hearings on the 2020 presidential election ahead of January 6, which is the day Congress will certify the results.
"I'm gonna do what I'm gonna do and that's fight for what I believe is that we need an improvement in our election system whether other people join or not is up to them," Brooks said.