Senate Republican leaders failed Wednesday to head off a floor fight over immigration, even as they continued to try to limit the damage a prolonged debate might cause on an $80.6 billion supplemental war spending bill.

A vote Wednesday evening on a nonbinding resolution revealed that a majority of the Senate does not believe immigration issues should be debated during consideration of a funding bill for U.S. troops in Iraq and Afghanistan. The vote was 61-38 in favor of the resolution.

But as of press time, Sens. Larry Craig (R-Idaho) and Barbara Mikulski (D-Md.) were undaunted and actively moving forward with debate on their amendments to make it easier for undocumented immigrants to work legally in the United States.

Earlier, both Senators rejected an offer from Senate Majority Leader Bill Frist (R-Tenn.) to debate a comprehensive immigration package later this year.

“Everybody wants to wait until later this summer or this fall. That is too late in my estimation,” Craig said. “Our bills are a great deal more time sensitive and more mature pieces of legislation.”

But the vote on the nonbinding resolution served as a reliable test of how Senators would vote if and when the Craig and Mikulski amendments come up for a final vote.

“I think it will be less likely that they will pass,” said Senate Appropriations Chairman Thad Cochran (R-Miss.).

Senate Majority Whip Mitch McConnell (R-Ky.) added that the vote made it more likely that “there’ll be a major effort to discourage other amendments on immigration on this bill.”

Craig, Mikulski and others began contemplating whether to offer their immigration amendments to the supplemental spending bill after the House added controversial immigration provisions to its version of the bill. The House language would require states to adopt tough standards for issuing drivers’ licenses and make it harder for federal courts to grant political asylum petitions.

Meanwhile, as of press time, Frist was still trying to get a unanimous consent agreement to limit the number of immigration-related amendments that could be debated on the bill, according to Senate GOP aides.

As the immigration debate began Wednesday afternoon, Sen. Dianne Feinstein (D-Calif.) threatened to “take some time” debating Craig’s proposal to make it easier for undocumented immigrants to get work visas in the agricultural industry.

“This is a very controversial bill that can have a huge impact on the number of people coming across the border,” said Feinstein.

Feinstein said she had several amendments she would offer to Craig’s “AgJobs” proposal and would also bring up a separate amendment to reauthorize a bill that helps states pay for illegal aliens housed in their jails.

But Craig warned Feinstein that any delay on AgJobs could negatively affect her home state.

“She better be careful because she will collapse her agricultural economy if we make a misstep,” Craig said on the Senate floor. “We don’t need to debate immigration on the floor for five days unless the Senator from California wants to drag it out.”

Feinstein also complained about the breadth of Mikulski’s amendment, which would exempt seasonal undocumented workers from the cap on those who can obtain unskilled work visas in the United States.

Feinstein joined Sen. John Cornyn (R-Texas) in co-sponsoring the nonbinding resolution that discouraged the Senate from debating immigration issues while the war spending bill was on the floor.

Cornyn said that immigration issues would be better debated in the Judiciary Committee first, and that the current debate would result in the supplemental getting “bogged down and diverted in an immigration debate, which, I think frankly, we’re not ready for.”

Senate Democrats worried Wednesday that opening the floor to immigration measures would cause a Republican Senator, possibly Sen. Johnny Isakson (Ga.), to offer an amendment similar to the House’s drivers’ license provision. However, one senior Senate GOP aide indicated that Isakson had agreed to stand down, principally because the proposal was likely to fail in a Senate vote.

Cochran, however, ominously predicted that any inclusion of the House immigration language would foment a filibuster on the Senate floor, particularly if the House provisions were included in any House-Senate conference report.

“It would go down,” Cochran said of the entire war spending bill.