Senate debate on the $350 billion tax-cut package begins Monday amid great uncertainty about what the final bill will contain.

No votes are scheduled for today as each side gets one hour to begin making its case. Debate on amendments will begin Tuesday with no votes before noon.

Much has changed in the tax bill since President Bush first made his $726 billion proposal. Finance Chairman Chuck Grassley (R-Iowa) had to pare down Bush’s original plan — including its elimination of dividends taxes — to get a package through his panel last week.

Following a deal with moderate Sen. Olympia Snowe (R-Maine), who sits on the Finance Committee, the bill would now exempt from taxes the first $500 of dividend income and then 10 percent after that. It also contains $88 billion in tax increases, such as cracking down on offshore corporations and removing a tax break for U.S. citizens working overseas.

Those offsets kept the committee bill within the $350 billion limit set for the Senate by the budget resolution.

Despite the compromise, Senators on both sides of aisle dislike the bill and will try to change it before debate ends.

Senate leaders hope to finish the bill Thursday or Friday.

Some Republicans may try to drop the offsets, saying that a bill designed to cut taxes should not also raise them.

Other Republicans, including Majority Leader Bill Frist (Tenn.), have said they will fight to up the dividend exclusion.

Most Democrats think the package is already too big, given the growing size of the federal deficit, and they would like to see significant aid for cash-strapped states.

For his part, Bush is working hard to persuade some swing Senators and the public that his plan is what the weakened economy needs.

Bush wants the Senate to bump its package up to at least the $550 billion figure the House approved Friday.

Democratic Sen. Ben Nelson (Neb.) has signaled he would support a larger dividend provision than that which was reported out of committee.

In a move perhaps designed to put pressure on Nelson, Bush is visiting his home state of Nebraska today.

“Nelson is supportive of it being higher than $350 billion, but with him it doesn’t matter the size as much as the content,” his spokesman, David DiMartino, told The Associated Press. Nelson wants more state aid, particularly for Medicaid.

Republican Sens. Snowe and George Voinovich (Ohio) have said they will not support a total package exceeding $350 billion while GOP Sens. Lincoln Chafee (R.I.) and John McCain (Ariz.) voted against the budget resolution.

Democratic Sen. Zell Miller (Ga.) has been on board with the president’s plan from the beginning and Sen. Blanche Lincoln (D-Ark.) voted for the compromise language in the Finance Committee.

Beyond the tax package, the Senate will also consider the global HIV/AIDS bill and debt limit legislation this week.

“The Majority Leader expects late nights and roll call votes throughout the week,” this week’s whip notice warned. “If necessary, the Senate may remain in session next weekend in order to complete action on all these items.”

Meanwhile the House, which already dispensed with its tax-cut legislation, will work on bills from the suspension calendar Tuesday and Wednesday, including a resolution urging the United Nations to lift economic sanctions against Iraq.

Also on Wednesday the House will debate the Pension Security Act of 2003.

On Thursday, which is Former Members Day, the House will consider a bill to reauthorize the National Transportation Safety Board.

The House is not scheduled to be in session Friday.