WASHINGTON—The Senate unveiled final details of a broad tax bill—and its 10-year price tag of $858 billion—and began debate Thursday night on the package, a significant step after two years of gridlock over how to treat expiring tax cuts enacted under former President George W. Bush. Without action, income taxes on nearly every American are due to rise on Jan. 1.

The Senate has moved quickly after Mr. Obama and Republican leaders unveiled the package Monday, with a key test vote now scheduled for Monday. The bill is expected to pass with support from most Senate Republicans and a substantial number of Democrats, after lawmakers agreed to extend expiring subsidies for ethanol and other alternative-energy sources. Backers now include Senate Majority Leader Harry Reid (D., Nev.), who had been withholding support over the bill's tax cuts for upper-income taxpayers.

But in the House, Democrats were in open revolt. In a closed-door gripe session, they chanted "Just Say No," capping a remarkable day of political theater before passing a nonbinding resolution that said the tax agreement shouldn't be considered in the House unless changes were made.

That resolution isn't seen as a threat to the tax deal, which includes a two-year extension of current tax rates for all income brackets, not just for income up to $250,000, as Democrats want. But the rebellion represented essentially a "no confidence" vote in the White House on a crucial issue.

Anger focused on the tax treatment of wealthier Americans and the fact that House Democratic lawmakers were frozen out of negotiations that produced the agreement. "This is not an acceptable package. We want a better deal,'' said Rep. Peter DeFazio (D., Ore.). House Speaker Nancy Pelosi (D., Calif.) suggested that she didn't want to kill the tax package, just change it. "We will continue discussions with the president and our Democratic and Republican colleagues in the days ahead to improve the proposal before it comes to the House floor for a vote," she said in a written statement.