House approval means the measure is headed to Obama's desk for his signature.
The House vote followed a delay Thursday. The Hill reported the House had been ready to vote on the rule governing debate on the bill, but the measure was pulled when leaders realized it likely would fail.
"We're just trying to work out some kinks," Rep. Jim McGovern, D-Mass., one of the tax bill's floor managers, said.
He called the decision to pull the procedural measure "a bump."
The Senate Wednesday approved the package on an 81-19 vote. Among other things, the package would extend for two years lower tax rates enacted during George W. Bush's administration that are set to expire Dec. 31, extend unemployment benefits for 13 months, cut the payroll tax by 2 percent for a year, lower a restored estate tax and extend several tax breaks included in the 2009 economic stimulus package.
"I think it'll be taken care of," McGovern said of the matter, adding that he didn't think the delay would go beyond Thursday.
The tax compromise has angered and divided House Democrats. As a measure of appeasement, the House leaders agreed to vote on a change in the estate tax provision, which would be lowered under the tax package to a rate of 35 percent on amounts exceeding a $5 million exemption. Some Democrats said as written that does nothing to spur the economy while benefiting the wealthy, but Republicans said it is necessary to allow family businesses to be passed from one generation to the next.
Under the rule approved Wednesday, lawmakers would vote on an amendment to the estate tax provision of the tax bill. If the estate tax amendment failed -- which is expected -- then the House would vote on the Senate bill. Liberals objected to that procedure, saying they wanted a chance to reject the entire bill, not just the estate tax provision.