Inside the Senate GOP resistance to Trumpcare

Sens. Ted Cruz, Rand Paul, and Mike Lee are among those against the bill.

"I have got concerns because people I respect in this area believe that it's fallen short," he said.

The Senate has 52 Republicans and needs a simple 51-vote majority to pass the Obamacare replacement package. They can have up to two party members defect, as Vice President Mike Pence can cast a tie-breaking vote. While the bill is still working its way through the legislative process, ABC News counts at least 10 senators who have either said outright they can’t support it in its current form, or have voiced uncertainty.

Portman's home state of Ohio is one of 32 that accepted the Affordable Care Act's Medicaid expansion, which brought in more recipients by raising the percentage of the poverty level above which people could join. He said he reiterated to Pence that he was concerned the bill, which would eventually cap states’ Medicaid payments, would harm his constituents.

"I raised the same concerns I've raised all along," Portman said.

Portman, along with three other senators whose states expanded Medicaid, is part of a growing group of senators who have expressed concerns about the bill in its current form because of the way it deals with Medicaid.

"They’re getting it done," Thune said of the House’s process. "My guess is that kind of the basic sort of components of the bill -– Medicaid reforms and refundable tax credits and things like that -– are all elements that I suspect will be in any package."

He did not address the fact that many Republicans on both sides of the aisle, including the conservative House Freedom Caucus, have voiced concerns with exactly those provisions.

Roberts, the third senator in the Pence meeting, said he told the administration officials present that they could "maybe sell this a little better" and emphasize GOP-favored concepts that have broader support like the ability to buy insurance over state lines.

Trump sought to sell the deal when he tweeted assurances that the bill’s drafting was going along smoothly.

But a few hours earlier, Sen. Tom Cotton, an Arkansas Republican who has supported Trump more than many of his colleagues, voiced his own skepticism of the bill using Trump's preferred medium.

Cotton later told ABC News' Jon Karl in an interview that he feared the current version of the House bill might make the health care system worse, not better.

But at the very least, Spicer added, “no matter where you are, especially on the conservative side, you cannot possibly believe that the current healthcare system is an effective program."

"I'm inclined to support anything because of Obamacare being such a failure," he said.