Governors from both parties are pushing for a quick but lasting deal to avert the fiscal cliff and they are asking that any cuts to state aid be accompanied by fewer federal mandates. Following a Tuesday meeting at the White House between President Barack Obama and members of the National Governors Association, the state executives kept their message bipartisan and vague, without endorsing any one approach or plan.

“What we all agree on is something’s gotta get done,” said Delaware Gov. Jack Markell, the chairman of the NGA. Markell, a Democrat, said none of the governors want to see taxes go up on middle class families.

“The president certainly wants a deal. … He’s going to work as positively as he can,” he said.

The governors said that they were prepared to take some cuts to help close the deficit, but want more flexibility on programs such as Medicaid in return.

Utah Gov. Gary R. Herbert, a Republican, said that the uncertainty about the cliff is creating “havoc” in the states. He said his budget alone could take a $500 million hit. “States are willing to do our part. We understand this is going to be a shared sacrifice. … States are willing to do more with less. We’re asking for more flexibility.”

Gov. Mike Beebe of Arkansas said shared sacrifice is OK, up to a point.

“We don’t need cuts on the federal level that merely require tax increases on the state level,” the Democrat said.

Wisconsin Gov. Scott Walker ducked several questions about his future plans, including a possible 2016 presidential run, and declined to take any shots at Obama.

“We’re not elected to fix all the problems in Washington,” the Republican said.