The ideal package would have been larger than the current one, and it would have been better tailored. The $120 billion cut in the payroll tax, for example, will apply to the portion paid by workers, not companies. The Congressional Budget Office and other analysts have said that cutting the workers’ portion provides less bang for the buck because individuals are likely to save some portion of the money. Cutting the employers’ portion subsidizes hiring.

But politics prevented the best kind of payroll tax cut. Republicans did not want one larger than the $120 billion, one-year cut in the package. Administration officials wanted the political benefit of having that whole sum apply to individual workers. The resulting compromise will help the economy, but not as much as it could have.

Initial estimates by economists suggested that the overall legislation would reduce the unemployment rate by one-half a percentage point to a full point over the next year, compared with allowing all the tax cuts to expire and passing no new stimulus. By the end of 2012, the decline could be up to 1.5 percentage points, economists said.

On the other hand, the unemployment rate will still probably be near 8 percent by the end of 2012, when the current package expires, and the two parties will get to have this fight all over again.

What’s the early line on that fight? Republican officials hope that Democrats will again find it hard to let all the tax cuts expire in the name of letting some expire. White House officials hope the economy will have improved enough by then to help Mr. Obama win re-election — and to allow him to threaten, credibly, to veto any bill that includes a tax cut for the wealthy.

There is also one big unknown looming over the whole debate: the deficit. This week’s deal, of course, will worsen the deficit. In the short run, many economists believe a larger deficit is better than the alternative. As Ben Bernanke, the Federal Reserve chairman, said during a recent “60 Minutes” interview, “We don’t want to take actions this year that will affect this year’s spending and this year’s taxes in a way that will hurt the recovery.”

Yet Mr. Bernanke and other economists usually add another point. Any additional spending now, they say, should be paired with future deficit reduction. Otherwise, the long-term deficit will continue to rise, and nervous investors may eventually demand that the federal government pay higher interest rates. Interest rates remain low for now, but they did rise on Tuesday, after the compromise was announced.

The problem is that raising the deficit — be it through high-end tax cuts or a new stimulus program — is a lot easier than cutting it. Strange as it may sound, some of the only fiscal conservatives in Washington this week have been liberals who would be willing to let everyone’s taxes rise. And they seem unlikely to win on this issue.