Prospects for the success of the bill, which angered a broad swath of congressional Democrats, brightened Tuesday when influential House Majority Leader Steny Hoyer said there were now “compelling reasons” to support it.

"The vote in the Senate indicates an urgency that is felt by a broad spectrum that the middle-income taxes not be increased come Jan. 1," Hoyer said in a briefing with reporters. "Rarely do you see that big a number" in support of a bill, Hoyer said.

If true, it means that bubbling liberal opposition to the compromise worked out between the White House and the G.O.P. leadership has evaporated.

President Obama and Democrats in general have campaigned for two years against extending the Bush-era tax cuts to the wealthiest of Americans.  But the compromise allows for a two-year extension, a step Republicans insisted on in exchange for renewing tax cuts for lower earners as well as extending unemployment benefits for several million Americans. The Senate might vote final approval of the tax bill late Tuesday or Wednesday. The House vote would be expected to come before the week is up.

Meanwhile, Hoyer and Rep. Patrick Murphy (D-PA) say later this week they will introduce a stand-alone measure to repeal the Don’t Ask Don’t Tell ban on gays openly serving in the U.S. military.

Supporters of the bill hope House passage of the repeal would pressure the Senate to also approve the bill before the lame duck session expires at the end of the year.