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 Grant HatchOvernight Finance: NAFTA defenders dig in | Tech pushes Treasury to fight EU on taxes | AT&T faces setback in merger trial | Dems make new case against Trump tax law | Trump fuels fight over gas tax What sort of senator will Mitt Romney be? Not a backbencher, even day one Lawmaker interest in NAFTA intensifies amid Trump moves 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."