Centrist Democrats from swing states may balk at supporting President Obama's healthcare reform package, Sen. Richard ShelbyRichard Craig ShelbyTrump defends handling of coronavirus as Democrats hit him during debate Overnight Health Care — Presented by American Health Care Association — Lawmakers raise alarms over Trump coronavirus response | Top official warns virus appears inevitable in US | Democrats block two Senate abortion bills San Francisco declares state of emergency over coronavirus MORE (R-Ala.) predicted Tuesday.

Shelby, the ranking member of the Senate Banking Committee, warned Democrats might risk overreaching as Republicans had if they force through a controversial healthcare bill.

"There are a lot of people in the swing states, there are a lot of moderate Democrats that are going to be very, very uncomfortable with rushing through a health care policy that could be something that would break the back of America," Shelby said.

In particular, Shelby acknowledged Sens. Ben Nelson (D-Neb.) and Claire McCaskill (D-Mo.), who were suggested by host Joe Scarborough.

Shelby also cautioned against using the reconciliation process to budget for healthcare legislation.

"There will be hell to pay for any of this stuff because we know, as Republicans, we did some things that probably should have gone through the regular order, and it didn't," the onetime Democrat said. "And healthcare should certainly go through the regular order not through the reconciliation process."