Daschle said the bill, which has been blocked in the Senate since the end of last year, would be "high on the list" of legislative priorities "after the break."
Daschle's comments appear to dash hopes immigration advocates had expressed earlier Tuesday that the Senate would try to reconsider the bipartisan legislation--which also contains an extension of the 245(i) visa program--in time for President Bush's trip to Mexico this week to discuss migration and other issues.
"The Senate's passage of the border security bill before President Bush goes to Mexico ... would indicate our seriousness in tackling important security concerns," Jeanne Butterfield, executive director of the American Immigration Lawyers Association, said in a conference call with reporters.
Bush appealed Tuesday to the Senate to show the "leadership" necessary to pass the measure.
Daschle and Senate Minority Leader Trent Lott, R-Miss., support the bill, but Sen. Robert Byrd, D-W.Va., has indicated he has substantive concerns about aspects of the measure dealing with the 245(i) program, which enables certain immigrants already in the United States to remain in the country while awaiting citizenship.
However, the House already has approved the Senate bill, both with and without the 245(i) extensions, so Daschle could bring up either version for amendment, a chief Senate cosponsor said.
"It's up to Sen. Daschle," said the cosponsor, Senate Judiciary Immigration Subcommittee ranking member Sam Brownback, R-Kan.
As for a Bush administration proposal to merge the U.S. Customs Service and the Immigration and Naturalization Service, which includes the Border Patrol, and place enforcement activities under the aegis of the Justice Department, Brownback said he did not know enough details of the plan to comment.
A spokesman for House Judiciary Chairman Sensenbrenner, whose committee is scheduled to mark up the chairman's INS restructuring legislation shortly after the spring recess, indicated likewise. But "from what details are available of Bush's plan, it would not negatively impact our legislation," he added.
However, Butterfield criticized the new homeland security plan as one "that has not been carefully or thoughtfully considered, and we're gravely concerned ...that stakeholders have not been consulted," Butterfield said.
Added Frank Sharry, executive director of the National Immigration Forum: "This would [cause immigration] enforcement to be completely divorced from adjudications, which we think would likely make a bad situation worse. It seems to us to be going in exactly the wrong direction."