Sen. Charles Schumer (D-N.Y.) (J. Scott Applewhite/AP)

Senate Democrats plan to draft a budget blueprint that calls for significantly higher taxes on the wealthy, oil and gas companies and corporations doing business overseas, reopening a battle over taxes Republicans had hoped to lay to rest with the “fiscal cliff.”

For nearly four years, Senate leaders have ducked their legal duty to craft a comprehensive budget framework. Now, however, Democrats see the budget process as “a great opportunity” to pursue additional tax increases — and to create a fast-track process to push them through the Senate, Sen. Charles E. Schumer (D-N.Y.) said Sunday on NBC’s “Meet the Press.”

“There’s going to have to be some spending cuts, and those will be negotiated,” Schumer, the No. 3 Democrat in the Senate, said in an interview after the show. “But doing a budget is the best way for us to get revenues.”

The announcement comes days after House Republicans offered to forgo a potentially damaging clash over the federal debt limit, saying they would vote this week to permit the government to continue borrowing through mid-April. In return, House leaders demanded that the Senate revive the traditional budget process, by which the two chambers adopt their own blueprints and work out differences in conference committee.

With the offer, the GOP backed off its hard-line stance that any increase in the debt limit be paired with spending cuts of equal size — “a major victory for the president,” Schumer said.

The move also suggests a desire by Republican leaders to create a more orderly forum for the partisan clash over record budget deficits. White House political adviser David Plouffe welcomed that move Sunday in an appearance on CBS’s “Face the Nation.”

“I think it’s a significant moment that the Republican Party now has moved off their position that the only way they’re going to pay their bills is if they get the correct kind of concessions,” Plouffe said. “I think we’d all be better served to go back to a little bit more regular order in Congress so we’re not careening crisis-to-crisis.”

Fresh deadlines loom in March: Sharp automatic spending cuts are due to hit the Pentagon and other federal agencies at the beginning of the month. And a temporary funding measure will expire at the end of the month, shutting down the government unless Congress acts.

But the developments of the past few days suggest that both parties are looking to continue the argument without sparking panic in financial markets and causing unnecessary harm to the broader economy.

Reviving the budget process is critical to that effort.

Because they are fraught with political pitfalls, budgets are protected from filibuster in the Senate, so Democrats could pass a budget without Republican votes. A budget blueprint is also the only way to create a fast-track process for deficit reduction, known as reconciliation, which is also protected from filibuster.

House Republicans are eager to draft a reconciliation bill to cut spending on federal health programs and to overhaul the tax code, in part by cutting rates. And Democrats are eager to draft a reconciliation bill that would raise additional revenue, in part by limiting tax breaks for wealthy individuals, oil and gas companies and multinational corporations.

During the fight over the “fiscal cliff,” Congress voted this month to raise rates on income over $450,000 a year. Republican leaders, including Senate Minority Leader Mitch McConnell (R-Ky.), argued that should end the fight over taxes.

But the “fiscal cliff” measure is projected to generate only about $600 billion over the next decade, well short of President Obama’s goal of $1.6 trillion. On Sunday, Schumer said Democrats plan to fight on.

“We’ll have tax reform . . . but’s it’s going to include revenue,” he said. “It’s a great opportunity to get us some more revenue to help” replace the automatic spending cuts, which are scheduled to slice nearly $1 trillion out of agency budgets over the next decade.