Story highlights Back-to-back scandals for House GOP this week underscored their challenges in the new Congress

House Speaker John Boehner is facing calls for a coup that have grown louder

Boehner's support of Rep. Steve Scalise is necessary for his survival, but could hurt the GOP brand

House Speaker John Boehner's not waiting until New Year's Day for a hangover -- his headache is already here.

Back-to-back House Republican dramas in the final week of the year are the latest indication that many of the issues the GOP hoped to leave behind when they take full control of Congress next week — an unruly base and scandal-prone members — will continue to dog them in the new year, and might even kick off 2015 with an attempted coup on the Speakership.

Though Boehner was successfully able to convince Rep. Michael Grimm to resign on Monday after pleading guilty to a felony tax evasion charge last week, Rep. Steve Scalise, the majority whip now embroiled in scandal over a 2002 address he gave to a white supremacist conference, remains a tougher mess to clean up, leaving the speaker open to attack from the left and the right.

In a coordinated move, both Boehner and his deputy, House Majority Leader Kevin McCarthy, issued back-to-back statements of support for Scalise on Tuesday afternoon. But the fallout of his appearance at a conference of the European-American Unity and Rights Organization — a group founded by the infamous white supremacist and former grand wizard of the Ku Klux Klan David Duke — continued into Tuesday night as multiple national newspapers issued op-eds calling for Scalise to resign.

But some in the party's right flank are aiming their fire at Boehner.

Facing calls for a coup from his conservative base in next week's speaker race that grew louder on Tuesday, Boehner can't afford to let Scalise, a former Republican Study Committee chairman and one of his strongest links to that conservative base, go.

While this wouldn't be the first time that Boehner's faced a conservative challenge for his speakership, many on Tuesday began to speculate that the controversy surrounding Scalise, and Boehner's handling of it, may breathe new life into a challenge.

Tom Davis, a former Virginia congressman and chairman of the National Republican Congressional Committee, warned that starting the new Congress with a coup attempt would be "catastrophic" for a party hoping to sell itself as the capable and effective alternative to Democrats in the 2016 elections.

"[A speakership coup] would be the worse thing that could happen to the party. It would show they can't govern their own caucus, let alone the government," he said. "When people unhappy with Obama look to Republicans for a governing party, this is the last thing they want to see."

He added: "They have an opportunity to really produce some good legislative outcomes. Why would you jeopardize that at this point by starting of with turmoil?"

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Boehner's backing of Scalese -- a move some on the right see as hypocritical -- put him in a precarious position heading into the speaker election.

"This has gotta make John Boehner nervous," one House GOP aide with ties to leadership told CNN of the continued controversy surrounding Scalise.

That's because, if the fallout for Scalise continues, Boehner may not be able to afford to keep him.

Scalise's alleged sins aren't unfamiliar to the GOP and exactly the kinds of associations the party is looking to avoid as it seeks to broaden its appeal to minority voters and improve its brand for the upcoming presidential elections.

Democrats seized on the development, with a member of Congressional Black Leadership on Monday calling for Boehner to investigate the situation.

On Tuesday, a spokesman for House Minority Leader Nancy Pelosi called the development "deeply troubling." And a House Democratic leadership aide said the party plans to keep up the pressure on Boehner and Scalise in the coming weeks.

There are also growing indications that even standing by Scalise may not do Boehner much good in terms of getting a handle on an unruly caucus that's only grown more frustrated with leadership since the midterms.

They recently emerged from a vote on a government funding bill crying mutiny because it failed to adequately oppose President Barack Obama's unilateral move on deportations and ObamaCare. Conservatives saw Scalise's vote for the "cromnibus" as the latest in a long line of his betrayals of the base.

Despite repeated attempts, however, conservatives have never been able to lock down the necessary votes to oust Boehner, and a viable opponent, or even send the speaker contest to a second round of votes. But Boehner's support for Scalise, some say, may cause enough ire within the base to reinvigorate the effort.

What conservatives see as unequal treatment for a member of leadership has incensed many still smarting over their dismaying loss in the Mississippi Senate race primary.

During that race, Sen. Thad Cochran's primary challenger, state Sen. Chris McDaniel, took heavy flak from the national and local GOP establishment for being billed alongside a white nationalist as a headliner at a conference that he never ultimately attended.

McDaniel has said there's a clear "double standard" at work, and in a text message Monday night suggested that double standard could further stoke the ire of conservatives against leadership.

"Conservatives are driven and inspired by principles, not personalities. We therefore seek consistency with our elected officials. To the extent that they are not consistent, anger is the inevitable result," he said.

"So yes, many will be angry."

Indeed, conservative commentator Eric Erickson, hosting Rush Limbaugh's talk-radio show on Tuesday, said he's heard "pretty credibly" that conservatives have 25 of the 29 votes they need to oppose Boehner and at least send the speaker race to a second round.

And he urged some of the incoming GOP freshmen to join the cause.

"Many of these guys ran saying, 'I oppose John Boehner — are they actually going to stand up now" and vote against him, Erickson asked. "I think this could undermine the leadership — and I think that's a good thing."

And Fox News Host Sean Hannity amplified the calls for a coup in a Tuesday statement to Brietbart News , declaring that it's "time for new dynamic leadership" in the House and naming South Carolina Rep. Trey Gowdy, the chairman of the House select committee investigating the Benghazi attacks, as his pick.

Gowdy, however, quickly declined, underscoring the problem conservatives have encountered time and time again when attempting to overthrow Boehner — they've found no clear alternative to run against him.

And many conservatives came out Tuesday offering their full support for Scalise, including Iowa Rep. Steve King, and Boehner's allies say they remain confident he'll be fine in the election.

"These guys thrive on making trouble," Davis said of conservatives, "but I don't think Boehner's ever been stronger within the conference."

But Republicans on Capitol Hill admit the next week could make or break both Boehner and the GOP's chance at starting off the new Congress, and the path to the 2016 elections, on the right foot.

"Maybe after this week [a challenge to his speakership] could be a more serious conversation — but everybody I've talked to seems to think he's in a very solid shape," the House GOP aide said.

But the aide added: "It just depends on how Steve does. Boehner has kind of, in a way, tied himself to Steve now."