The administration is also betting that employers will back the proposal, especially in states where their taxes would otherwise go up. Michigan, for instance, owes the federal government $3.7 billion it borrowed to pay unemployment benefits. Under current law the state would be forced to pay $117 million in interest to the federal government this fall, and the federal tax on employers would automatically step up each year to repay the debt.

The state’s newly elected Republican governor, Rick Snyder, has been lobbying for relief; his press secretary, Sara Wurfel, said that while they would need to see the details of the plan, they would “very likely welcome the much-needed relief.”

Robert Gibbs, the White House press secretary, said, “We are giving help to some states who have had to borrow and not been able yet to pay back.”

The states are in a tough spot. Many entered the recession with too little money in their unemployment trust funds, and theyquickly ran through what little they hadas unemployment rose and remained stubbornly high month after month.

With their own trust funds depleted, 30 states borrowed $42 billion from the federal government to continue paying unemployment benefits.

The federal stimulus act gave states a break on the interest for those loans for nearly two years, but that grace period ended Dec. 31. That has left hard-hit states, which have already laid off employees, cut services and raised taxes, facing an estimated $1.3 billion in interest payments to Washington due this fall.

Even more worrisome, to some states, is that current law would effectively raise taxes on employers by about $21 per worker in nearly half the states so they could start paying down their debt, which states worry would put pressure on businesses that have already been reluctant to hire in the downturn.

In his budget, officials said, Mr. Obama will call for deferring interest payments on the debt and postponing the automatic tax increases. Then, in 2014, to bring that money back into federal coffers, the administration proposes to raise the minimum level on which employers pay taxes.

Current law requires states to collect unemployment taxes on at least the first $7,000 of income; that minimum has not been raised in decades.