Updated

The House and Senate appear to be on a collision course over President Obama's controversial tax plan, after House Democrats voted to block the package from coming to the floor in its current form.

Though the vote was not binding, the House Democratic caucus on Thursday approved a measure by Rep. Peter DeFazio, D-Ore., effectively rejecting the GOP-negotiated deal unless and until a majority of Democrats support it. One Democratic leadership aide said the vote "shows how much the White House screwed this up."

Senate Republican Leader Mitch McConnell, meanwhile, told Fox News he expects the Senate to take up the bill anyway without any substantive changes Thursday afternoon. He predicted the measure would pass, a belief echoed by a number of Senate Democratic aides interviewed by Fox News. But that would send the bill straight to the House, where some members are mounting a rebellion.

"If it's take it or leave it, we'll leave it," said Rep. Lloyd Doggett, D-Texas, after the caucus vote Thursday, adding that he thinks House Speaker Nancy Pelosi will take her cue from the caucus.

Pelosi, releasing a statement shortly after the vote, said only that the party would "continue discussions" with Republicans and the president to "improve the proposal" before a floor vote.

"Democratic priorities remain clear: to provide a tax cut for working families, to create jobs and economic growth, to assist millions of our fellow Americans who have lost their jobs through no fault of their own, and to do this in a fiscally sound way," she said. The White House said that Congress was working through the "normal process" of debating legislation.

The Democrats' resolution specifically stated that the tax package in its current form "should not come to the House floor for consideration."

Rep. Jim McDermott, D-Wash., said "it's a pretty clear message. We don't like the bill."

The vote came after 54 Democrats, led by Rep. Peter Welch of Vermont, signed a letter in opposition to the tax cut deal. The 54 Democrats, by themselves, would not be enough to block the package in the House, depending on how much support it gets from Republicans. But the caucus vote could shake things up.

Rep. Jim Clyburn of South Carolina, the House's No. 3 Democrat, said when asked what comes next, "I don't know. We'll wait and see."

The White House continues to face an uphill climb in convincing his party to get on board with the package. The administration appeared to be breaking through after Vice President Biden visited the Hill on Wednesday, and some Democrats left acknowledging that the package could have enough support to pass.

As of Thursday, Democrats were all over the map. Most Republicans seemed to be standing by the negotiated package, but a few prominent conservatives were peeling off and criticizing it as too expensive.

Speaking Thursday at a White House event promoting American exports, President Obama said the vote will determine whether the economy "moves forward or backward."

The president again pressed Congress to pass the agreement, saying it has the potential to create millions of jobs. He said if it fails, Americans would see smaller paychecks and would result in fewer jobs.

The Associated Press contributed to this report.