The Senate rejected a Republican effort on Tuesday to establish a limited program allowing low-income students to use federal money for private school tuition.

The vote was 58-41 and came as leaders in both parties signaled a desire to wrap up work on President Bush's high-profile education legislation within the next few days.

At the same time, Sen. Tom Daschle, D-S.D., announced that Democrats would use their new leverage as the majority party to press the White House to increase its commitment of federal funds for public education.

"Reform is impossible without resources," Daschle said in his first public challenge to Bush since becoming majority leader last week. "And we will continue to press for resources" when the House and Senate begin compromise talks. He said he had told the president last week "it was not our desire to complete this work until we have some understanding about the degree of resources that will be made available."

Sen. Judd Gregg, R-N.H., advanced the effort to give low-income students in failing schools funds to apply toward the public or private school of their choice.

By whatever name, he said, "Choice, portability, vouchers to use the pejorative term, it's all about one thing: giving America's children the opportunity to learn. And it's especially about low-income children locked in the inner city whose only opportunity is to learn."

But Democrats argued the proposal was fraught with constitutional problems and would siphon off funds -- already in short supply -- that are needed in the public schools.

"The idea that this is going to open the door to parents whose children are in failing schools and want a way out is raising false hopes," argued Sen. Edward M. Kennedy, D-Mass. "Before we have crocodile tears all over the floor about leaving no children behind, we're already leaving children behind," he said. He contended that Bush's budget proposals fall far short of full funding for the government's program of assistance to schools with low-income populations.

Overall, Bush's legislation would require states to administer annual math and reading tests to students in grades three through eight. Schools with low test scores would receive additional aid, but if a school failed to show enough progress after two years, low-income students would be free to transfer to another public school. After three years, the same students would be permitted to use federal funds for tutoring or transportation to another public school, but not for private school tuition.

All schools would receive some additional flexibility in their use of federal funds as part of the effort to improve.

But the legislation also would create a pilot program in which seven states and 25 school districts could receive far greater flexibility in their allocation of federal funds, a key demand of the White House and Republicans in bargaining with Democrats.

Gregg and other Republicans sought a similar approach with vouchers -- a demonstration program in which a limited number of low-income students in failing schools would become eligible for federal grants they could use for private school tuition. The amendment would have created programs in up to 10 cities and three states, and Gregg argued that Democrats should readily agree to the proposal if they believed claims that parents would not want to make use of the opportunity.

"If we don't get on the path of correcting these schools which are failing and we do not get on the path of giving children in those schools options to learn in an environment which is conducive to learning then we will lose another generation and as a nation we can't afford that," Gregg said.

Democrats argued otherwise. "Vouchers undermine our public schools. Vouchers leave children behind. Vouchers mean less accountability and vouchers are a distraction from the hard but essential work of ensuring all public schools are good schools," said Sen. Patty Murray, D-Wash.

The amendment drew the support of 38 Republicans and three Democrats. There were 46 Democrats, 11 Republicans and one independent opposed.

In the political dynamic of the education bill, approval of Gregg's amendment would likely have complicated White House efforts to win passage of the overall bill. Democrats led by Kennedy negotiated an agreement with the White House on a basic framework for overhauling the federal system of aid to education, and have generally worked together to fend off major changes.

The exception is in the area of funding, where Democrats have prevailed with several amendments adding to the cost of the bill. Overall, the measure calls for about $30 billion for elementary and secondary education for the next fiscal year, nearly $11 billion more than Bush has proposed.