Thus, entitlement spending, which poses the biggest long-term challenge to the federal budget, accounts for only a sliver of the cuts. That leaves more than $70 billion in cuts to be applied over the next seven months to the roughly two-fifths of the budget that is devoted to discretionary spending, including the military, education and dozens of other categories.

In a matter of weeks the cuts would cascade through the government, delaying snow removal on the Tioga Pass in Yosemite National Park, for example, and keeping an aircraft carrier battle group docked in Norfolk, Va., rather than steaming through the Persian Gulf.

“The cut is so big and over such a short period of time that there’s no way to avoid all the operational and program harms,” said Daniel I. Werfel, controller of the White House budget office.

These cuts would probably not be confined to 2013. Even if President Obama manages to persuade Congress to raise new revenue, he has said he would replace only half of the spending cuts with tax increases, in essence accepting a half-trillion dollars in cuts over 10 years. That would be on top of more than $1 trillion in cuts already enacted by the Budget Control Act, which created the sequester in 2011 as part of a deal to raise the country’s statutory borrowing limit.

A comprehensive deficit-reduction deal, which is currently moribund but is still both Congress and the White House’s stated goal, might mitigate the impact by including fast-growing programs like Medicare and Medicaid in the cuts. But belt-tightening, for now, appears to be the new normal.

In private, Capitol Hill staff members and members of Congress have admitted that there are no viable plans on the horizon to delay or offset the cuts. At best, Congress might be able to pass a bill giving agencies more discretion in carrying out the budget cuts. But that is opposed by the White House because officials fear that such a change would give lawmakers a false sense that they had done much to ease the pain of the cuts, when in fact, budget officials say, little would have changed.