Washington, D.C. ? As the Senate neared passage of President Barack Obama’s tax cuts package Tuesday, a House Democratic leader acknowledged that momentum is building, despite opposition to the $858 billion compromise.

Many Democrats argue that the compromise between the White House and Republican leaders disproportionately benefits the wealthy. The deal would extend tax cuts first passed during the George W. Bush administration for all taxpayers, including those earning beyond $250,000.

But Sen. Mitch McConnell, R-Ky., the Senate GOP leader, warned that changing the legislation with just days remaining in the legislative session could upend the tenuous agreement.

“This agreement is not subject to being reopened,” McConnell said, as the Senate prepared to pass the bill. “I hope that our friends in the House will understand that that’s the best way to go forward — simply pass the Senate bill, get it down to a president who supports the understanding.”

The Senate worked late Tuesday on the measure and leaders expected Senate passage today. House leaders were meeting Tuesday night to map their strategy on the bill.

The White House remained confident the deal would hold as the president telephoned lawmakers to secure their votes.

“We are on a path toward getting this agreement through the House and ultimately to the president’s desk,” said Press Secretary Robert Gibbs.

Meanwhile, prominent Republicans, including former Massachusetts Gov. Mitt Romney, who is widely expected to run for president in 2012, criticized the package for contributing to the federal debt. Romney joined other Republicans, including former Alaska Gov. Sarah Palin and commentator Rush Limbaugh, in opposing the compromise.

The proposal would extend tax cuts for two years and continue unemployment benefits through 2011 for 7 million jobless Americans who otherwise would see their extended benefits expire. The Obama administration projects it could create 2 million jobs.

“What some are calling a grand compromise is not grand at all, except in its price tag,” Romney wrote in USA Today. “The total package will cost nearly $1 trillion, resulting in substantial new borrowing at a time when we are already drowning in red ink.”

To many Democrats, the deal represented a lopsided tradeoff. They are expected to seek to amend an estate tax provision that drew particular opposition because it exempts up to $5 million in inheritances from the 35 percent tax.

Democrats prefer a 45 percent estate tax on inheritances larger than $3.5 million, as the House approved last year.

“I don’t think we’re basing what we want to do on a threat by Mr. McConnell,” said Rep. Louise Slaughter, D-N.Y., chairwoman of the House Rules Committee.

Yet as House Democrats met behind closed doors late Tuesday evening, leaders acknowledged they had little leverage to change the legislation that appears headed toward completion by the end of the week.

Final Senate passage is expected today after consideration of several amendments. Senate Republicans will offer two amendments to permanently extend all tax breaks, repeal the estate tax, and pay for the $56 billion cost of unemployment benefits with spending cuts elsewhere.

The Senate voted 83-15 Monday to advance the bill, a move seen as putting pressure on the House.