The Ryan measure also revives a controversial plan to turn the Medicare program for the elderly into a voucher-like system for future beneficiaries born in 1959 or later. Critics say the idea would mean ever-spiraling out-of-pocket costs for care, but Ryan insists the plan would inject competition into a broken system.

‘‘This is an uncompromising, ideological approach to our budget issues,’’ said the Budget Committee’s top Democrat, Chris Van Hollen of Maryland. ‘‘The American people voted, and they resoundingly rejected the approach that is now taken, once again, for the third year in a row, in this Republican budget.’’

Fresh from passing the 2013 wrap-up measure on Wednesday, the Senate was turning to Murray’s plan, which would add nearly $1 trillion in new taxes over the coming decade in an attempt to stabilize the $16 trillion-plus national debt.

It’s the first budget debate scheduled by Senate Democrats in four years. Democratic leaders have seemed intent on protecting members from a slew of politically troublesome votes forced by Republicans and don’t seem to have suffered from charges that they've been shirking their budget duty.

But Murray’s plan would actually increase government spending — on top of a ‘‘baseline’’ that already assumes automatic budget increases averaging more than 5 percent a year — after accounting for the $1.2 trillion cost of repealing the automatic cuts, known as sequestration. That means the net cuts to the deficit would amount to just a few hundred billion dollars in a federal budget estimated at $46 trillion or so over the coming decade.

Murray’s position is that the automatic cuts were designed to prod Washington into action on the debt and were never intended to take effect. By that math her budget promises $1.85 trillion in lower deficits after 10 years. She points out that Republicans on a 2011 deficit ‘‘supercommittee’’ used the same math when describing their proposals.