The Democratic proposal would establish a 30-percent minimum tax rate on incomes over $1 million to raise about $54 billion over 10 years. It would raise $1 billion more by subjecting tar sands oil to a tax to pay for oil-spill cleanups and by ending a business tax deduction for the cost of moving equipment overseas. The remaining $55 billion would come from $27.5 billion in defense cuts from 2015 to 2021 and $27.5 billion in farm-subsidy cuts. The legislation is more a bargaining position than a solution. Republicans have said they will not accept any new taxes in a deal to head off the so-called sequester — across-the-board cuts to defense and domestic programs of 5 percent to 8 percent and totaling about $1 trillion over 10 years. But Senate Democratic leaders said Thursday that their party must rally support around an alternative to try to move negotiations forward. “This bill is an important chess piece,” said Senator Charles E. Schumer of New York, the No. 3 Democrat in the Senate. Speaker John A. Boehner of Ohio on Thursday repeated his demand that the Senate take the first steps to replace the spending cuts before the House considers its move, but no one predicted that the Senate Democrats’ proposal would rally the bipartisan support needed to overcome a near-certain Republican filibuster and reach the House. “I would hope that we can get to 51 votes, and that majority would rule,” said Senator Barbara Mikulski, Democrat of Maryland, the chairwoman of the Senate Appropriations Committee. “I’m confident we will have the majority — if not the totality — of the Democratic caucus.” Senate Democrats emerged from a protracted lunch meeting over the plan voicing only grudging support. Senator Max Baucus of Montana, the chairman of the tax-writing Finance Committee, said he worried that wringing savings from farm subsidies now instead of in a broad farm bill would make it harder to pass an overhaul of agricultural programs that has been stalled for nearly a year. Senators Tom Harkin, Democrat of Iowa, and Bernie Sanders, independent of Vermont, denounced the 50-50 mix of cuts and taxes, after Democrats have swallowed far more spending cuts than tax increases over two years of deficit-reduction efforts. Republicans dismissed the proposal as a worthless gimmick. “This is not a solution — even they know it can’t pass; that’s the idea,” said Senator Mitch McConnell of Kentucky, the Republican leader. “It’s a political stunt.” The White House praised the package. Jay Carney, the press secretary, called it a “balanced plan to avoid across-the-board budget cuts that will hurt kids, seniors, and our men and women in uniform.” “Republicans in Congress face a simple choice,” he added. “Do they protect investments in education, health care and national defense, or do they continue to prioritize and protect tax loopholes that benefit the very few at the expense of middle- and working-class Americans?” As the cuts approach, warnings of disaster are growing increasingly dire. The Senate Appropriations Committee released a barrage of letters from agencies spelling out how the cuts would be meted out: 600,000 low-income women and children dropped from federal nutrition programs; meat and poultry plants forced to close because of furloughed federal inspectors; deep cuts to the poor school systems that rely most heavily on federal assistance; delayed permits for oil and gas production; and shorter seasons, reduced operating hours and possible park closings in the national park system. Job losses could reach 750,000 this year, said Representative Chris Van Hollen, Democrat of Maryland. While Republicans and Democrats agree the cuts would be destructive, neither side seems ready to negotiate a solution. Senator Harry Reid of Nevada, the majority leader, reached out to Mr. Boehner on Thursday. Mr. Boehner said he told Mr. Reid what he has been saying publicly: The House will look at what the Senate can produce. “This sequester was the president’s idea,” Mr. Boehner said. “His party needs to follow through on their plans to replace it.”