By a 50-49 vote along party lines, the Senate fell short of the 60 votes necessary under its rules to effectively prevent major changes to a Democratic version of the bill. Mr. Bush has threatened to veto that version because it does not meet his demands for the new management powers.
The upshot is that Republicans will have more time to push for an alternative that the president will accept.
Democrats, however, said the decision would simply mean more delay on a bill that lawmakers had once hoped to send the president by Sept. 11.
"I mean, this is our opportunity either do it or not, and I would just hope that we could do it and move on," said Senate Majority Leader Tom Daschle, D-SD.
Bush sought to give a lift Thursday to an alternative drafted by Sens. Phil Gramm, R-TX, and Zell Miller, D-GA., that would slightly modify the labor powers and make more than 15 other changes to the Democratic bill in areas ranging from intelligence to immigration.
"The purpose of homeland security should be to protect lives, not jobs," said Miller, a conservative Democrat who frequently breaks with his party's leadership.
The proposal would preserve the president's existing power to exempt workers from union coverage for reasons of national security, but would add requirements for employee and advance congressional notification.
Gramm said he and Miller were "still working on about 20" senators of both parties in an effort to gain a majority for their alternative. "We come down to one issue: are you with the president or are you against the president?" Gramm said.
Mr. Bush planned to urge lawmakers to pass the alternative during an appearance Thursday at an Office of Homeland Security command center across town from the White House, spokesman Ari Fleischer said.
"The president believes that this compromise will be a way to help the Senate out of the impasse in which it finds itself," Fleischer said.
Democrats have loudly objected to Bush's demand for new personnel powers, contending they would gut the federal civil service and protections provided by union membership.
Moderate Democrats, including Sens. John Breaux of Louisiana and Ben Nelson of Nebraska, were pushing an alternative focused on the union issues - one that would preserve the president's national security waiver authority but allow workers a chance to appeal. About 43,000 of the proposed agency's workers now belong to unions.
Removing a worker from union coverage, Breaux said, "may be necessary but at least the workers ought to have an opportunity to make their case that they're not part of a national security enterprise. That's all we're asking for."
Republicans said such appeals would only mean more delays in moving personnel around to confront terrorist threats.
"We probably couldn't do that," said Senate Minority Leader Trent Lott, R-MS.
As negotiations continued, Senate debate ground on for a third week on a bill lawmakers had once hoped to finalize before the Sept. 11 anniversary.
Sen. Robert Byrd, D-WV, was pushing an amendment that would require congressional approval in three separate steps during the 13-month transition to a new agency, which would be composed of 22 existing entities including the Coast Guard, Customs Service,
Border Patrol, Transportation Security Administration and Secret Service.
"Congress should not buy into the empty promises of a one-time fix," Byrd said. "We must sign up for the long haul."
But the bill's chief sponsor, Democrat Joseph Lieberman of Connecticut, said that would "take the heart out of this proposal" by delaying and complicating the transition unnecessarily. Congress will have ample opportunity in the future, he said, to make changes in the new department.
"It will be a work in progress," Lieberman said.