Story highlights John Kasich said there should be a bipartisan push to shore up the insurance markets

"Of course there's a willingness to work across the aisle," the Ohio governor said

Washington (CNN) Republican Ohio Gov. John Kasich welcomed the collapse of the Senate Republican health care bill Tuesday, saying it would come as a "relief" to many.

Kasich, in an interview on CNN's "The Lead," told Jake Tapper that members of both parties should seize the moment -- and that his fellow Republicans were going the wrong way to consider a full repeal of Obamacare without a substantive and simultaneous replacement.

"I think there are people who are breathing a sigh of relief," Kasich said.

On Monday evening, two conservative senators announced they would oppose the Senate GOP bill to repeal and replace large portions of Obamacare. That announcement meant Senate Majority Leader Mitch McConnell did not have enough support to pass the bill. He announced shortly thereafter that the Senate would attempt to consider a full repeal of the Obamacare legislation, but with a two-year delay on the repeal going into effect. By midday Tuesday, enough senators had announced their opposition to that plan to ensure it would not pass.

Read More