Romney has been under fire from conservatives over the law — it's generally seen as one of his greatest liabilities in a presidential bid. This past weekend in New Hampshire, Romney said of the law, "Some things worked, some things didn't and some things I'd change." 

In a recent interview with The Hill, former Pennsylvania Sen. Rick Santorum (R), another rumored 2012 contender, was much more forceful in his critique of Romney, suggesting that the former governor's embrace of healthcare reform in Massachusetts should all but disqualify him for the Republican presidential nomination next year. 

As national Democrats have strategically praised Romney's Massachusetts plan, at least some Republicans have come to Romney's defense. In an interview earlier in the week, Sen. Orrin HatchOrrin HatchCan Trump rebound after failure on healthcare bill? Overnight Finance: US preps cases linking North Korea to Fed heist | GOP chair says Dodd-Frank a 2017 priority | Chamber pushes lawmakers on Trump's trade pick | Labor nominee faces Senate US Chamber urges quick vote on USTR nominee Lighthizer MORE (R-Utah), a Romney supporter, said he doesn't think conservatives will hold the Massachusetts plan against him if he makes another presidential bid next year.

"It's hard to think that conservatives will not [support him] because Romney basically is a conservative, there's no question about that," Hatch said in an interview with ABC News. "But he's a smart conservative, somebody who's practical."