It remains unclear how long sequestration will last: it was designed to be onerous to force a compromise on an alternative. But Mr. Obama and Republicans indicated on Friday that the cuts would probably remain in place at least until the end of the fiscal year, Sept. 30.

Democrats, led by the president, express confidence that in coming months public pressure will force Republicans to relent on revenue, especially as cuts to the military begin to be felt. But Republican leaders have said they will stand firm against tax increases, suggesting that they have won at least a temporary victory on reducing the size of the government.

In his weekly address on Saturday, Mr. Obama said the Republicans had “decided that protecting special-interest tax breaks for the well off and well connected is more important than protecting our military and middle-class families from these cuts.”

“I still believe we can and must replace these cuts with a balanced approach — one that combines smart spending cuts with entitlement reform and changes to our tax code that make it more fair for families and businesses without raising anyone’s tax rates,” Mr. Obama said.

In the Republican response, Representative Cathy McMorris Rodgers of Washington State, said: “The problem here isn’t a lack of taxes. This year alone, the federal government will take in more revenue than ever before. Spending is the problem, which means cutting spending is the solution. It’s that simple.”

According to the nonpartisan Congressional Budget Office, total government spending is falling compared with the size of the economy but will rise again in the next decade. That growth will be driven by the entitlement programs as more baby boomers retire, not by discretionary spending.