Two top senators reached broad agreement Tuesday on a bipartisan $31 billion anti-terrorism bill that exceeds President Bush's request by nearly $4 billion and sets the stage for a clash between the White House and Congress.

The Senate Appropriations Committee was expected to easily approve the measure on Wednesday. That same day, Republican leaders are hoping to push a roughly $29 billion version of the package — this one with Bush's blessing — through the House.

The Senate bill provides the same $14 billion that Bush proposed for the Pentagon. However, in one of several ways that the bill would reorder White House priorities, it would pour $3 billion more than the $5.3 billion Bush wanted into grants for firefighters, port security, bolstered bioterrorism preparedness and other domestic security programs.

Senate Appropriations Committee Chairman Robert Byrd, D-W.Va., who wrote the measure with Sen. Ted Stevens, R-Alaska, said hearings the panel held with state and local officials justified that increase.

"One message is clear, namely, we are not prepared," Byrd said in a written statement.

But while not using the word "veto," White House officials said the Senate measure was too expensive.

"President Bush asked Congress to resist the temptation to overspend," said Trent Duffy, spokesman for the White House budget office. "The House has done that and should be commended. The Senate should exercise the same restraint."

The Senate measure contains $5.5 billion to help rebuild New York from the Sept. 11 attacks, as Bush and the House also proposed. Also like the House, it includes $200 million in aid for Israel and $50 million for Palestinians, plus funds for Pell grants for low-income students and for upgrading state and local election systems — none of which Bush sought.

The Senate measure also contains $73 million for flood and storm relief for West Virginia, the Midwest, Maryland and Kentucky. And while it includes up to $28.5 million for the Colombian government to battle rebel groups — less than the House and Bush proposed — it puts tight restrictions on how the money could be spent.

The Senate bill would cut the $10 billion loan program for ailing airlines that Congress provided last fall to $4 billion. But it ignores a House proposal to eliminate part of the $5 billion in grants that were provided to airlines, and another House plan — since dropped — to double the $2.50 per flight segment airline security ticket tax.

The Senate bill provides the full $4.4 billion Bush requested for the new Transportation Security Administration, which oversees aviation security. The House cut that amount by $400 million, citing a bloated bureaucracy.

Transportation Secretary Norman Mineta said Tuesday that the cut would slow hiring and equipment purchases.

"Without the full level of funding, passengers at the nation's airports will face long lines and flight delays," Mineta said.

Democratic leaders hope the Senate will approve the bill before lawmakers' scheduled departure Friday for a weeklong Memorial Day recess.

An aide to Stevens, the Appropriations panel's top Republican, said he opposed two provisions of the bill.

One would make Homeland Security Director Tom Ridge's post a job requiring Senate confirmation, a proposal that continues Byrd's clash with the White House over Ridge's relationship with Congress. The other would require Bush to accept all the domestic spending in the bill — including the funds the Senate would add.

The House version of the bill has wide bipartisan support.

But as a result of related disagreements, Democrats — and perhaps some Republicans — were expected to try blocking the House from even considering the measure. These disputes included GOP efforts to attach language to the bill paving the way for an increase in federal borrowing and limiting overall spending this year.