House Republicans and some conservative Democrats are poised to hold Attorney General Eric Holder in contempt of Congress on Thursday for withholding documents in the investigation into botched Operation Fast and Furious, which let guns slip into the hands of drug cartels.

House Speaker John Boehner is pressing ahead with a floor vote that is almost certain to pass, with the majority Republicans expected to get the backing of some Democrats. At least five Democrats so far have said they plan to vote to hold Holder in contempt, and sources tell Fox News as many as 11 appear ready to break ranks.

Those Democrats are largely conservative-leaning lawmakers facing perilous political circumstances in their home districts. But regardless of motive, their support only increases the odds that the nation's top law enforcement official will be held in contempt of Congress come Thursday.

The vote against a key Obama administration official comes on the same day the Supreme Court is due to announce its decision on the constitutionality of President Obama's health care law, the administration's key domestic agenda achievement. The contempt vote, however, is expected to take place sometime in the afternoon, several hours after the Supreme Court decision.

If the contempt measure passes, it would touch off a whole new legal process -- in which a U.S. attorney would be called upon to convene a grand jury to consider the allegations and whether to indict, though with Holder at the helm it's unclear how that would play out.

The two sides also will likely continue to battle over the documents at the heart of the dispute as Obama tries to lock them down by claiming executive privilege.

Several Democrats indicated Wednesday they don't buy that argument.

"While Republicans and Democrats argue over the scope of the people's right to know what happened, the attorney general has decided to withhold relevant documents," Rep. John Barrow, D-Ga., said in a statement announcing he would support the contempt resolution. "The only way to get to the bottom of what happened is for the Department of Justice to turn over the remaining documents, so that we can work together to ensure this tragedy never happens again."

Other Democrats to announce an anti-Holder stance include Reps. Nick Rahall, D-W.Va.; Collin Peterson, D-Minn.; Jim Matheson, D-Utah; and Mike McIntyre, D-N.C.

Matheson said the public, Congress and the family of Border Patrol Agent Brian Terry -- whose murder scene included weapons from the botched anti-gunrunning operation -- "deserve answers."

The White House, though, slammed Republican leaders for pressing ahead, accusing them of engaging in "political gamesmanship" with a vote they claim could have been avoided.

"(Republicans) have shown very little interest in reaching a resolution. Instead, they've chosen a path of political confrontation and theater," White House Press Secretary Jay Carney said Wednesday. "It is politics."

Carney said Democrats are "hopeful" a last-minute arrangement can be reached, but expressed doubt that would happen.

Boehner said Thursday that "we are going to proceed." The House Rules Committee teed up a Thursday floor vote on contempt by taking up two related contempt resolutions Wednesday afternoon.

That meeting was contentious.

GOP Rep. Darrell Issa, chairman of the House Oversight and Government Reform Committee and the lawmaker leading the contempt charge, told the rules committee that he's pressing ahead because Holder has not fully complied with requests for a full account.

"Over the last year-and-a-half, the committee has found the Department of Justice uncooperative every step of the way," said Issa, R-Calif.

But Rep. Elijah Cummings, ranking Democrat on the House oversight committee, asked the panel and Boehner to put off the vote.

"I urge you to take a step back," said Cummings, D-Md. "I am convinced ... that this can be worked out."

Rep. Louise Slaughter, D-N.Y., the top Democrat on the rules committee, added, "This has all the trappings of a witch hunt."

The vote is proceeding despite a last-ditch attempt by Obama administration officials on Tuesday to work out a deal.

A source familiar with those talks told Fox News that the Republicans met with administration officials twice Tuesday -- at the Justice Department and at the White House. The Justice Department showed GOP staff 14 documents on the failed anti-gunrunning operation, totaling about 30 pages.

Republicans apparently thought the offer was not good enough.

But the move prompted criticism from the White House.

"This was a good faith effort to resolve this while still protecting the institutional prerogatives of the Executive Branch, often championed by these same Republicans criticizing us right now," said White House spokesman Eric Schultz.

Republicans have accused the Justice Department of stonewalling all along, and claim the contempt vote is a last-resort move to extract documents about the operation -- specifically documents from February 2011 and beyond that speak to why the administration might have initially claimed it did not allow guns to "walk" across the U.S.-Mexico border. The administration later retracted that claim.

Fox News' Chad Pergram contributed to this report.