BOSTON – Governors hamstrung by the sluggish economic rebound in their states and bound to balance their own budgets are pressing anew for Washington to step up with more help, even if it means adding to the nation’s red ink.

Republicans and Democrats alike wrestled with how to capitalize on a fledgling rebound as they talked dollars and sense at their summer meeting just days into a new budget year and as the economy shapes dozens of gubernatorial races across the country.

“All states still are facing tough fiscal situations even though I do believe we’re in recovery,” said West Virginia Gov. Joe Manchin, a Democrat who’s taking over as chairman of the National Governors Association.

Added Gov. Jim Douglas, R-Vt., the outgoing chairman: “Governors have done what is necessary to get through this” — repeatedly cutting budgets, restructuring government, laying off workers and draining rainy day funds.

But both men said states can’t continue to climb out of the recession alone, and a majority of governors renewed their bipartisan appeal for Congress to pass stalled jobs legislation that includes billions of dollars in aid to states.

Just days before the new budget year began July 1, the House and Senate failed to complete legislation that would have extended, through June 2011, important parts of the federal stimulus program enacted last year to provide unemployment insurance and help offset recession-driven cuts to education, health care and public safety.

The measure offered $35.5 billion for unemployment benefits for the long-term jobless and $16 billion for Medicaid, the public health care program for the poor. It also would have added an estimated $33 billion to the deficit.

Even so, several Democratic and Republican governors suggested in interviews and during panel discussions that the short-term gain was worth the long-term pain.

Maryland Gov. Martin O’Malley, a Democrat facing a tough re-election fight, said that without Washington’s assistance, “the danger of a double-dip recession is greater.”

But Wyoming Gov. Dave Freudenthal, also a Democrat, said money from Washington wasn’t the answer. “Each of us has to figure out a way to pare back the public’s expectation of what government’s going to pay for.”

Governors headed to Boston for the weekend ready to share ideas on a range of issues, from health care to alternative energy to education. But the economy and how to capitalize on signs of recovery dominated the discussions.

States have suffered for two straight years as collections from sales, income and property taxes came in lower than expected when people stopped spending money, lost their jobs and the housing market tanked. Governors also saw demand for state services soar.

While the federal government reports signs of economic growth, recovery is slower in the states. A report last month by the governors’ association and the National Association of State Budget Officers found that state fiscal conditions continue to deteriorate.

States are expected to have faced $296.6 billion in shortfalls between the 2009 and 2012 budget years, and the report found that the new budget year will be just as challenging despite the expectation of modest increases in tax collections.

That means governors will have to cut spending or raise taxes to make up for expected budget gaps, steps certain to slow the economic recovery further.

There are political realities to the states’ economic challenges. This fall, 37 states will elect governors; a majority of those races already are competitive. The economy is dominating contests across the country, and Democrats are on defense in a slew of economically struggling states.