Indiana, for example, reported saving or creating 13,232 education jobs with its stimulus money, but Cris Johnston, the director of the government efficiency division of the state budget office, said that it was difficult to say whether the state would have actually lost those jobs without the money.

“We can’t make the statement that they were created or retained,” Mr. Johnston said. Indiana, he said had followed federal guidelines in reporting how many full-time jobs were paid for with the stimulus money, which also paid for education supplies and other expenses. And while New York City officials have said the stimulus helped them save thousands of teaching jobs, it would have been politically difficult for Mayor Michael R. Bloomberg to actually lay off that many teachers while running for re-election.

Hard hats could surpass teachers next year, as more construction projects get under way. In Florida, for instance, one of the biggest infrastructure projects is its plan to build the Indian Street Bridge in Martin County. But with a big, complex project like that, it takes a while before construction can start. That project, which will cost more than $72 million, claims to have saved or created just one job so far.

An analysis by The New York Times of the grants and contracts in the stimulus showed that as of the end of September, only 7 percent of the work had been completed and 9 percent was more than half done, while 46 percent was less than half done and 38 percent had not begun.

The jobs announced Friday were created by about $159 billion in grants, loans and contracts made available to the states. About $37 billion of that amount has been paid out so far.