Still, McConnell said he believes some reform is necessary - and he thinks there's bipartisan support. He called for incremental adjustments to a health system he called the best in the world.
"The way forward ought to be to start over," said McConnell.
Burr said he favors slowing down and looking at the whole issue of health care in the country. His plan would raise money by taxing health benefits and use the revenue to give people tax credits to buy their own care.
"We would like to see this process slow down. We would like to see more consideration given to the content, the substance of the bills," he said.
Congress is currently in summer recess. The health care debate is expected to heat up when lawmakers return to Washington next week.
Republicans in the minority hope to slow Democrats. They say a public option will cost too much.
"The President, in the other party, says we're doing this to save money. And yet it's going to cost an additional trillion dollars," offered McCain.
President Obama has not presented a detailed plan for reform - instead leaving Congress to hash out the details. Republicans say he should show his cards.
"There's so many targets out here. Why didn't the President actually lay something on the table and say, 'But here's what I'm for,'" offered Burr.
Democrats are also using healthcare to attack Burr leading up to next year's campaign. They've accused him of holding invite-only and pay-to-see town hall meetings on the issue.
"North Carolinians should have some real questions about a senator whom they have to pay to see, whether it's a $2,000 steak dinner in DC with healthcare industry lobbyists or $50-30 or however much it is for a town hall event in Raleigh," offered Kerra Bolton with the NC Democratic Party.