White House counselor Kellyanne Conway said Wednesday that while President Trump and Vice President Pence may have their "imprimatur" on the GOP's new healthcare bill, she wouldn't refer to the plan as "TrumpCare."

"This is a piece of legislation also that has presidential leadership — he's really husbanding this through," Conway said on Fox News's "America's Newsroom."

"The president and vice president are all-in here. This is the [American Health Care Act], it has their imprimatur, and they are working on this more than anything day-by-day."

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"It's the American Health Care Act, and I think it's aptly named that for that reason. It wants everybody to have access to coverage, and that didn't happen under ObamaCare," she said.

"I'll call it 'TrumpCare' if you want to, but I didn't hear President Trump say to any of us: 'I want my name on that.' It's not about branding according to someone's name — it's serious business."

Trump blessed the new House bill to repeal and replace ObamaCare in a Monday-evening tweet where he referred to it as "our wonderful new healthcare bill," but cautioned that there will be "negotiation" as far as the final language.

The administration and Republican leadership are hoping the legislation will serve as a major policy victory to fulfill a campaign promise made by Trump and other Republican lawmakers, but there's been criticism from both sides complicating the path forward.

Some conservative Republicans have bashed the legislation for not going far enough to return healthcare to the private market, but there's also bipartisan concern about rolling back the Medicaid expansion under ObamaCare.