The bill could clear the Senate late Tuesday or early Wednesday, pressuring reluctant House Democrats to act on the deal the White House struck with the GOP. The $858-billion package extends tax cuts from the George W. Bush administration for two years and continues unemployment benefits for jobless Americans through 2011.
"The vote in the Senate indicates the urgency," Hoyer said of Monday's 83-15 procedural vote in the Senate. "When you look at this plan, there are some very good things in it."
House Democrats will meet behind closed doors Tuesday evening to strategize on the package that many representatives oppose, saying it favors the wealthy. Democrats particularly want to amend an estate-tax provision that exempts multimillionaires from the tax.
Hoyer said "significant concerns" remain about the deal.
Yet with tax cuts set to expire at year's end, lawmakers are increasingly aware there is limited time to alter the bill and avoid having the legislation pingpong between the House and Senate in the final days of the congressional session.
As if to underscore the risks, Sen. Mitch McConnell (R-Ky.), the minority leader, warned House Democrats not to change the agreement the GOP negotiated with the White House.
"This agreement is not subject to being reopened," McConnell said as the Senate moved toward a final vote Tuesday afternoon. "I hope our friends in the House will understand that's the best way to go."
Democrats would like to press forward on other legislative priorities before relinquishing their majority in the House, including a repeal of the military's ban on openly gay personnel -- a proposal that faces a difficult climb in the new year with greater Republican numbers in Congress.
"We're not going to walk away from any of the work that we have to do," said Sen. Harry Reid (D-Nev.), the majority leader. "We are going to complete our work no matter how long it takes in this Congress."
Outgoing Rep. Patrick Murphy (D-Penn.), the first Iraq war veteran to serve in Congress, has championed lifting the "don't ask, don't tell" ban and introduced a House measure that is scheduled for a Wednesday vote. A similar bill is pending in the Senate.
Congress also is considering votes on an arms treaty with Russia, a youth immigration measure and annual spending bills to keep the federal government running through next year.