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The stimulus-sized package aimed at averting a nationwide tax increase is cruising toward passage in the Senate, as House Democrats determine whether and how much to tinker with it.

"We don't have much time left," House Democratic Leader Steny Hoyer said Tuesday evening as he left a caucus meeting.

The Bush-era tax cuts will expire for all Americans if Congress doesn't act by the end of the year. Senate Majority Leader Harry Reid said his chamber will cast a final vote on the legislation Wednesday, after lawmakers signaled in a procedural vote Monday that they would send the bill to the House intact.

But House Democrats still have serious concerns about the contents of the package negotiated between President Obama and Republican congressional leaders. Hoyer would not rule out changes to the bill, saying Tuesday he wants the House to "reflect its view" on certain parts of the bill, namely the estate-tax provisions.

"There are strong feelings in the House," Hoyer said. "The temperature is pretty cold."

At the insistence of Republicans, the plan includes a more generous estate tax provision, which was repealed for 2010 but scheduled to kick in at a high rate at the start of next year. Under the compromise, the first $5 million of a couple's estate could pass to heirs without taxation, and an additional $5 million for the spouse. The balance would be subject to a 35 percent tax rate.

While House Democrats were furious the compromise package included an extension of the Bush tax cuts for the wealthy, they have since focused primarily on the estate-tax issue.

But Hoyer predicted the House would ultimately pass the bill. Lawmakers on both sides of the aisle say that despite their qualms about certain provisions of the $858 billion package, it would be economically damaging for the middle class to be hit by the tax increase scheduled for Jan. 1.

"There are some things I really don't like here, some things I intensely dislike, but we've got to keep in mind the overall effects of this package," Sen. Kent Conrad, D-N.D., told Fox News.

The package would extend the Bush tax cuts by two years. It would also renew a program of jobless benefits for the long-term unemployed that is due to lapse within days and enact a one-year cut in Social Security taxes.

House Democrats are scheduled to meet in a closed-door caucus Tuesday evening to discuss the package. Members could stay in session through the weekend to deal with the legislation. Any changes would have to subsequently be approved by the Senate before the bill can go to Obama for his signature.

Assistant Democratic Leader Dick Durbin of Illinois told CBS' "The Early Show" Tuesday that the wide margin by which the measure cleared the procedural vote should help facilitate its passage in the House.

"I think the House takes notice," he said, adding that he believes the bill will be passed by Christmas.

Durbin said he understands opposition to the bill from liberal Democrats outraged over the substantial relief given the wealthy in estate tax provisions. "In the spirit of the season, it does say 'God bless Tiny Tim and Donald Trump'," he said.

This week, several Democratic leaders said they may settle for a vote on an amendment that would impose a higher estate tax -- a vote that would face an uncertain outcome.

Under current law, the estate tax is scheduled to return next year with a top rate of 55 percent on the portion estates above $1 million -- $2 million for couples.

House Democratic leaders want to bring back the 2009 estate tax levels. That year, individuals could pass $3.5 million to their heirs, tax-free. Couples could pass $7 million, with a little tax planning, and the balance was taxed at a top rate of 45 percent.

Senate Republicans, however, warned that any changes to the estate tax provisions could unravel the deal.

"If the House Democratic leadership decides to make partisan changes, they will ensure that every American taxpayer will see a job-killing tax hike on January 1," said Senate Republican Leader Mitch McConnell of Kentucky.

The Associated Press contributed to this report.