BILOXI (AP) — A bipartisan group of governors said Saturday that the federal stimulus package helped states avoid deep budget cuts during the recession. But some at the National Governors Association convention said they’re not pushing for another infusion of cash from Washington.

‘‘I don’t think there’s an appetite for it,’’ Democratic Gov. Joe Manchin of West Virginia said.

Republican Gov. Haley Barbour of Mississippi agreed there’s no need for Congress to consider more aid to states any time soon. Most of the stimulus money disappears by December 2012, midway through the next budget year for many states.

‘‘We’re up on a very high peak that we’re going to have to get down off of when the stimulus money runs out,’’ Barbour said, noting that Mississippi has its largest-ever budget because of the federal funds.

Republican Gov. Jim Douglas of Vermont said state leaders would have liked fewer rules about how to spend the first batch of federal money, much of it directed to Medicaid and education.

‘‘Governors always want more flexibility because priorities are different from state to state,’’ Douglas said.

About half the nation’s governors were attending the convention on the Mississippi Gulf Coast. Some stayed home to work on budgets, including the group’s president, Pennsylvania Democrat Ed Rendell.

Manchin said lagging revenues prompted states to collectively cut budgets by $31.6 billion for the fiscal year recently concluded.