Democrats passed a resolution saying the tax package should not come to the House floor in its current form, but it was unclear how significantly the package might need to be changed. A formal House bill has not yet been drafted.
President Barack Obama's tax deal with Republicans would let rich and poor Americans keep Bush-era tax cuts that were scheduled to expire this month. Democrats are objecting to continuing tax cuts for the wealthy.
That vote came hours after Vice President Joe Biden made a visit Wednesday to Capitol Hill, urging fellow Democrats to accept a deal he argued was the best they could get.
"If it's take it or leave it, we'll leave it," said Rep. Lloyd Doggett, D-Texas.
Obama says the compromise was necessary because Republicans were prepared to let everyone's taxes rise and to block the extension of unemployment benefits for jobless Americans if they didn't get much of what they wanted.
The vote will at least temporarily stall what had seemed to be a grudging Democratic movement toward the tax package.
Many might have been able to live with a two-year extension of tax cuts for the wealthy, but drew the line at a surprise cut in inheritance taxes.
Although the wealthy will benefit from the tax cuts, so will middle and lower-income Americans.
A break on the payroll tax, which is proposed, could mean $1,400 more in the paychecks of those families earning $70,000 a year.
And the child tax credit would be extended, which means a mother of two earning minimum wage could claim a credit of $1,725 with the new tax cuts instead of seeing it drop to $263 without them.
Raising the direst alarm yet, the Obama administration warned fellow Democrats on Wednesday that if they defeat the plan, they could jolt the nation back into recession.
The Senate may vote on the bill as early as tomorrow.