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Both Mr. Lee and Mr. Paul cut even deeper than Mr. Toomey, with Mr. Paul’s budget even leading to a surplus over the next 10 years. But those plans, which relied on severe cuts to basic spending and entitlement programs, couldn’t even attract most Republicans. Mr. Lee’s plan was defeated 82-17, and Mr. Paul’s plan failed 83-16.

Democrats said there is no need for a budget this year, arguing that last year’s debt deal — which, unlike budgets, is actually signed into law — already sets the annual discretionary spending levels in law for 2013.

Under the terms of that deal, discretionary spending is slated to hit $1.047 trillion in 2013, $1.066 trillion in 2014, and grow to reach $1.234 trillion in 2021.

But the debt deal did not affect entitlement spending, which includes Medicare, Medicaid, Social Security and the other formula-driven programs that are the chief drivers of long-term deficits.

Instead of writing a budget this year, Sen. Kent Conrad, North Dakota Democrat and chairman of the Budget Committee, said Congress should go back and begin to debate the recommendations of the Bowles-Simpson fiscal commission, which called for tax increases and spending cuts in its December 2010 report.

“The place we agree is, we have a long-term problem for this country we must address,” Mr. Conrad said.

A key group of both Republicans and Democrats argues that report, written by former White House Chief of Staff Erskine Bowles and former Sen. Alan Simpson, is likely to serve as the basis of a year-end agreement when Congress faces the expiration of the 2001, 2003 and payroll-tax cuts; the looming automatic spending cuts from last year’s debt deal; and yet another debt-ceiling increase.

The Bowles-Simpson plan called for lowering overall tax rates but also for eliminating most tax loopholes, with some of the extra revenue going to reduce deficits. It also put limits on discretionary spending, including defense spending.

A version of the Bowles-Simpson plan was defeated 382-38 in the House in March.