“Bill Cassidy has repeatedly voted to slash seniors’ retirement benefits and turn Medicare into a voucher program that forces hundreds of thousands of Louisiana seniors to pay thousands more for their health care each year, and now he must own the new reckless G.O.P. budget proposal that does exactly that,” said Andrew Zucker, communications director for the Campaign for Louisiana, a Democratic group criticizing Mr. Cassidy, a House Republican running to unseat Senator Mary L. Landrieu.

Representative Steve Israel of New York, chairman of the Democratic Congressional Campaign Committee, said that in the coming weeks, the committee would be buying online advertising in competitive House districts, making automated phone calls and creating a new website, “Scandalous,” to tell of district-specific cuts.

“We are going to make this budget the centerpiece of the next seven months,” he said.

Republican leaders had considered not doing a budget this year, since spending cuts for the current fiscal year and the next were set in December with passage of a bipartisan plan. But House conservatives demanded a document they could take to their strongly Republican districts.

The new budget violates some tenets that both parties have tried to observe since the budget fights of 2011 and 2012. Those fights preserved a practice of cutting defense and nondefense programs almost equally while sparing the poorest Americans from the worst of the belt-tightening.

Mr. Ryan’s plan does not strike that balance.

In his plan, military spending through 2024 would actually rise by $483 billion over the spending caps established in the 2011 Budget Control Act “consistent with America’s military goals and strategies,” while nondefense spending at Congress’s annual discretion would be cut by $791 billion below those strict limits.

In all, Mr. Ryan said, spending would be cut by $5.1 trillion over the next decade. More than $2 trillion of that would come from repealing Mr. Obama’s health care initiative, the Affordable Care Act, a political move that has become much more difficult with the closing of the first enrollment period. More than 10 million Americans have gotten health insurance through the law, either through private policies purchased on insurance exchanges, through expanded Medicaid or private policies purchased through brokers but subsidized by the law.

As with past budget proposals, Mr. Ryan seeks to eliminate the Affordable Care Act’s Medicaid expansion, a $792 billion retrenchment, then turn the health care program for the poor into block grants to the states — saving an additional $732 billion over the decade. He would turn food stamps into a block grant program and cap spending, starting in 2020, cutting that program by $125 billion in five years. The budget relies on imposing new work requirements on food stamp and welfare recipients.