While economists almost universally support running large deficits to combat the kind of steep recession the country is grappling with now, they are increasingly expressing alarm at the prospect of sustained fiscal imbalances heading into a period in which the aging of the population will create huge budgetary strains because of the growing costs of the Medicare and Social Security programs.

Still, the deficit now seems likely to be so large that it will inevitably constrain Mr. Obama’s administration to some degree. At a minimum, it seems sure to force him to walk a line between maintaining the confidence of the financial markets, which could drive interest rates up sharply if they doubt his will or ability to improve the government’s financial condition in the long run, and various constituencies that will be pressing him to make good on his campaign promises.

Mr. Obama has so far not backed away from any of the big initiatives he ran on, including his plan to expand health insurance. On that issue, as on others, he has begun making a case that the economically prudent course is to invest now in addressing the nation’s big challenges rather than avoiding them in the name of saving money in the short run.

Mr. Obama was not specific about the size of the deficit he expects, beyond his reference to “a trillion-dollar deficit or close to a trillion-dollar deficit” for the fiscal year that ends Sept. 30. Aides said later that the estimate — in line with what economists have been anticipating given the economy’s rapid deterioration — did not include the costs of the proposed stimulus package, which could add hundreds of billions of dollars more to the red ink.

At $1 trillion, the deficit would not only shatter the largest previous shortfall in dollar terms — $455 billion last year — but it could also exceed the post-World War II-era record by the measure more meaningful in economic terms, the deficit as a percentage of total economic activity.

Diane Rogers, chief economist at the Concord Coalition, a nonpartisan organization that supports fiscal discipline, estimated that the deficit this year would hit 7 percent of the gross domestic product. The largest previous record in those terms was in 1983, when it hit 6 percent.

Mr. Obama declined to say on Tuesday whether the budget that his administration submits to Congress in February would be larger than the $3.1 trillion budget that President Bush submitted for the current fiscal year. He also did not offer any specific examples of how spending could be controlled, saying only that his advisers had been scouring the budget looking for programs that could be eliminated.