WASHINGTON — A once-quiet effort by governors to block the full repeal of the Affordable Care Act reached its climax in Washington on Tuesday, as state executives from both parties — who have conspired privately for months — mounted an all-out attack on the Senate’s embattled health care legislation hours before Republicans postponed a vote.

At the center of the effort has been a pair of low-key moderates: Gov. John R. Kasich, Republican of Ohio, and Gov. John W. Hickenlooper, Democrat of Colorado, who on Tuesday morning called on the Senate to reject the Republican bill and to negotiate a bipartisan alternative.

Just before Senate Republicans delayed a vote on the bill, Mr. Kasich denounced his own party’s legislation in biting terms, saying it would victimize the poor and mentally ill, and redirect tax money “to people who are already very wealthy.”

“This bill,” Mr. Kasich said, “is unacceptable.”

The mounting criticism from governors, including sharp denunciations from within President Trump’s party, helped stymie Republican efforts to marshal support in the Senate, and may have led, in a roundabout way, to the stalling of the measure this week.