The governors put aside their partisan disagreements and united in sending an urgent message to Congress.

“We do need to get our national deficit down,” Ms. Fallin said, “but give us flexibility. Relax those mandates. Give us some leeway.”

Gov. John W. Hickenlooper of Colorado, a Democrat, agreed that the federal deficit and debt were “a serious risk,” saying, “We recognize that we will have to be part of the solution and share the pain.”

But Mr. Hickenlooper said the across-the-board cuts were a blunt instrument. “Sequestration was originally designed by both the administration and Congress as something so odious, so repellent, that it would force both sides to a compromise,” he said.