Senate Democrats unveiled a plan Tuesday to save $21 billion over the next decade by eliminating tax breaks for the nation’s five biggest oil companies, a move designed to counter Republican demands to control the soaring national debt without new taxes.

With the proposal, Democrats sought to reframe the debate over debt reduction to include fresh revenue as well as sharp cuts in spending. For the first time, Democratic leaders suggested an equal split between spending cuts and new taxes — “50-50,” said Senate Majority Leader Harry M. Reid (Nev.).

That represents a larger share for taxes than has been proposed by either President Obama or the bipartisan commission he appointed to recommend how to cut the national debt.

So far, the Democratic tax agenda is focused on ending subsidies for big oil companies, a hugely popular proposal involving what Democrats see as a prime example of wasteful giveaways in the tax code. By raising the issue, Democrats are trying to force Republicans either to drop their rigid stance against new taxes or to defend taxpayer subsidies for some of the world’s most profitable corporations, including Ex­xon Mobil, Shell, BP, Chevron and ConocoPhillips.

The proposal came in response to remarks Tuesday by House Speaker John A. Boehner (R-Ohio), who said raising taxes is “off the table.” A day earlier, he gave a speech demanding more than $2 trillion in spending cuts in exchange for GOP support for an increase in the legal limit on government borrowing through the end of next year.

“We should not be drawing lines in the sand,” Reid told reporters Tuesday. “It has to be a fair approach to balancing the budget. We have to do something with domestic [programs]. We have to do something on defense. And, of course, we have to do a better job with taxes.”

Republican leaders affirmed their opposition to tax increases, whether through the elimination of oil company subsidies or any other changes in the tax code.

“We’re not going to raise taxes,” Senate Minority Leader Mitch McConnell (Ky.) told reporters. “That was decided in last November’s election. I think the American people pretty clearly believe that we have the deficit problem because we spend too much, not because we tax too little. ”

The clash over oil company subsidies is the latest flare-up in a broader battle over the most controversial budget issues: Republican demands for cuts to Medicare and other entitlement programs, and Democratic insistence on new revenue. In White House budget talks, which got underway last week and are expected to stretch into the summer, those two issues have been temporarily set aside as lawmakers from both parties work with Vice President Biden to try to identify areas of common ground.

Those talks continued Tuesday at Blair House, with the aim of easing passage of a significant increase in the debt limit, currently set at $14.3 trillion. Treasury Secretary Timothy F. Geithner has said he can pay the nation’s bills through Aug. 2 without fresh borrowing, but thereafter the United States would run the risk of default.

Despite the heated rhetoric on Capitol Hill, the atmosphere at Blair House was “significantly quite productive,” said Senate Finance Committee Chairman Max Baucus (Mont.), who represents his chamber’s Democrats in the talks. “Nobody suggested the speaker’s number [for spending cuts] or anything like that,” he said. “I sense in the room, we know what’s got to be done.”

The Blair House talks are the most prominent of several efforts aimed at producing a plan to control the debt. After stalling over the Easter break, the Senate’s “Gang of Six” — three Democrats and three Republicans — resumed meetings with renewed hope for an agreement later in the week.

Meanwhile, Senate Democrats are trying to draft their own budget blueprint, which could be put to a committee vote as soon as next week. The latest version, presented at a private lunch Tuesday, includes as much as $2 trillion in fresh revenue to reduce borrowing over the next decade, Democrats said, and avoids changes to Medicare and Social Security.

Facing pressure from cash-strapped voters to do something about surging gasoline prices, Democrats want to put a spotlight on highly profitable oil companies and cut off taxpayer subsidies to the firms.

Their proposal, which Reid said he could bring up for a vote next week, would close several long-standing tax loopholes, yielding roughly $2 billion a year in savings to be applied to lowering the deficit. It would affect only the five largest oil companies, excluding smaller producers.

Rolling back tax benefits for oil companies is a hardy perennial in Congress. In 2007, for example, Democrats capped their “100 hours” agenda by passing a measure that targeted oil companies’ eligibility for a manufacturing tax break that effectively lowered their corporate tax rates.

The break, adopted in 2004 to stimulate job growth by trimming tax rates for a range of manufacturers, gives oil companies and other manufacturers a top rate of about 32 percent instead of 35 percent. It is the biggest single budget item; its repeal would save $18 billion. Other oil company tax breaks are decades old.

But there is no evidence that eliminating them would help lower gas prices. “It is dishonest for any of us to say that there is some magic wand that could be waved and bring down gas prices,” said Sen. Claire McCaskill (D-Mo.).

Oil companies complain that they are being unfairly targeted while other businesses enjoy similar tax benefits.

“Targeting a specific industry or even a segment of that industry is what we would consider punitive and unfair tax policy, and it is not going to get us increased energy security, increased employment and certainly not going to lower the price of gasoline,” said Charles Drevna, president of the National Petrochemical and Refiners Association.

Republicans, meanwhile, have called for expanding domestic oil exploration and decreasing government regulation and fees on energy companies. The House voted last week to require the Obama administration to conduct offshore lease sales in the Gulf of Mexico and near Virginia. The House will vote this week on a proposal to lift Obama’s ban on offshore drilling.

Sen. Robert Menendez (N.J.), who sponsored the Democrats’ oil subsidies bill, highlighted the most recent quarterly profits from the five largest oil multinationals, which totaled $35.8 billion.

“Do you think working-class families should be the only people sacrificing to help lower the deficit?” Menendez said. “Do you think the wealthy and powerful should pay their fair share to help balance the budget, or should we simply let their high-priced lobbyists shield them from their responsibilities?”

Top executives from the five big oil companies are scheduled to testify before the Senate Finance Committee on Thursday.

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Staff writers Steven Mufson and Felicia Sonmez contributed to this report.