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“In an era of trillion-dollar deficits and long-term economic uncertainty, responsibly reducing spending is absolutely necessary,” Mr. Price said. “President Obama ought to stop putting false choices before the American people, when they are demanding meaningful and lasting reductions in the level of spending, so that we can get our economy rolling and more jobs created.”

A new poll suggests the public is not sharing the same level of alarm as Mr. Obama about the pending cuts. A survey by the Pew Research Center found that 29 percent of Americans have never heard of the sequester, and a full 40 percent believe the cuts should be allowed to go into effect. But a greater share, 49 percent, say the cuts should be delayed.

Democratic strategist James Carville said on MSNBC’s “Morning Joe” that if the cuts do take effect, Republicans are likely to get most of the blame.

“The sequester, not many people know what it is, but it sounds stupid and cruel,” Mr. Carville said. “Therefore, people think it’s a Republican thing.”

Among the government programs exempt from the sequester cuts are Social Security benefits (old-age, survivors and disability); all programs administered by the Department of Veterans Affairs; military personnel spending; interest on the federal debt; refundable tax credits; and many low-income programs, including Temporary Assistance for Needy Families, food stamps, child nutrition programs, mandatory funding under the Child Care and Development Fund, Medicaid, the Children’s Health Insurance Program, foster care and the Supplemental Security Income program.

Some budget analysts say the administration’s options for imposing the cuts are limited.

“From my read of the legislation, they have little [discretion],” said Patrick Knudsen, a budget expert at the conservative-leaning Heritage Foundation. “The president can prevent a pay cut for military personnel, but other than that, it appears the mechanism simply imposes the spending cuts across the board, account by account.”

Alex Brill, an analyst on fiscal policy at the American Enterprise Institute, said the administration has few good options.

“Among the affected accounts, there’s really very little flexibility that an agency has in terms of how to adjust itself,” Mr. Brill said. “It’s very difficult for an agency to reduce their number of employees, and very difficult for agencies to extract themselves from committed contracts. When you have to pay your workers, and you have to pay your contractors, you don’t have a lot of flexibility.”

Susan Crabtree contributed to this report.