NORTH LITTLE ROCK, Ark. (AP) — Congress shouldn't give up on finding ways to change the federal health overhaul in an approach that can win bipartisan support despite the collapse of the GOP effort to rewrite the 2010 law, Arkansas Gov. Asa Hutchinson said Tuesday.

The Republican governor said he was disappointed that efforts to rewrite former President Barack Obama's health care law were unsuccessful in the Senate after four senators said Monday they opposed the measure. Hutchinson said he thinks Democratic and Republican lawmakers in Washington can work together to address concerns with the law.

"I think you've got to be able to pull people together from both sides of the aisle and say we're going to have a bipartisan solution here to set the path for the future," Hutchinson told reporters. "I think that is the quickest opportunity with the most stability that will set us on the right path."

Arkansas expanded Medicaid under the health care law through a hybrid program that uses the expansion funds to place people on private insurance. More than 300,000 people are on the program. Hutchinson had raised concerns about the Senate bill before its collapse, saying it would shift too much cost to states like Arkansas.

Earlier Tuesday, Republican U.S. Sen. Tom Cotton said he supported Senate leaders' backup plan that calls for immediately repealing major parts of the health care law without an immediate replacement. That proposal also appeared to be short of the votes needed.

"If we can't develop a new system right away, because there's too many disagreements within the Senate, I still think we need to put the marker down," Cotton told Little Rock radio station KARN. "We need to fulfill the promise on which we campaigned for four straight elections, and then we can have another election because that bill on which we all voted two years ago has a two-year timeline on it."

Republican U.S. Sen. John Boozman also said he agreed with that approach.

"I support the Majority Leader's decision to move forward with a repeal of Obamacare with a transition period, so we can work together to replace this failed program with market-based solutions that will bring the changes that Obamacare, and all its broken promises, simply cannot deliver," Boozman said in a statement issued by his office.

Hutchinson, however, said repealing the law without a replacement would inject too much uncertainty in the health care system.

"I just don't think it's wise to say we're going to set an uncharted course," the governor said. "I think we have to know where we're going."