The tax package negotiated by President Barack Obama and GOP lawmakers is headed toward passage in the Senate even as House Democrats consider changes to the estate tax.

The bill could be passed and sent to the House by Tuesday. The Senate voted 83-15 Monday evening to advance the package, which would provide a two-year reprieve from tax increases scheduled to take effect on Jan. 1 at all income levels.

"This proves that both parties can in fact work together to grow our economy and look out for the American people," Obama said. "I recognize that folks on both sides of the political spectrum are unhappy with certain parts of the package and I understand those concerns. I share some of them. But that's the nature of compromise."

House Democrats are scheduled to meet in a closed-door caucus Tuesday evening to discuss the package. Last week, House Democratic leaders said they would not schedule a vote on the tax bill without changes to make it less generous to the wealthy.

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.