Michigan and California are likely to face a fresh round of budget woes when federal stimulus funds used as a fiscal crutch dry up, finance directors for the states said Friday.

Short-term budget gaps have battered states as revenues plummeted during the recession. Aided by about $250 billion in funds from the stimulus package expected through the end of next year, states managed to close the gaps this year. But both finance directors, speaking at a Pew Center on the States event in Washington, were pessimistic about their...