First, several Senate Republicans who opposed the first version of the House bill remain skeptical. Second, the Senate would likely have to change the bill significantly, perhaps in ways that might displease House Republicans when the two sides seek to reconcile the different versions.
House Republicans' new health care bill differs from the first one they proposed because it would remove a guarantee to cover people with pre-existing conditions. Under the new plan, states would have the option to request waivers from that requirement as long as they have another coverage option, like high-risk pools, which some experts have warned will raise costs for that cohort.
None of the holdout senators have to vote on the exact wording in the House version because the Senate would most likely change the bill before its own vote. The question is whether drastic changes would be necessary to get the skeptics on board.
For the Senate to pass a version of the Obamacare replacement bill, the two chambers would likely have to reconcile differences in what's known as a conference committee. It's not clear whether House Republicans who voted for their version of the bill would sign on to changes requested by senators and vice versa — a perennial concern for any legislation that goes through conference committee.
No Senate Democrats are expected to cross the aisle and vote for a replacement health care bill, meaning Senate Republicans could afford to lose only two votes from their 52 members and still pass the bill. Vice President Mike Pence would cast a vote in the event of a tie.
Cruz, who rejected the first House bill, suggested he would be open to using the new version as a springboard in the Senate but added, "I have a number of concerns, and I think many senators do."
"If the bill does pass the House, then it will come to the Senate, and it will be incumbent on us to continue to work to make it better," he added.
A spokesperson for Portman said the senator wants to see a better transition process for changing the way Medicaid is financed and more help for those receiving treatment for opioid addiction.
Capito, who opposed the House bill's Medicaid provisions, said through a spokesperson that the new version does not address her concerns. "She will work to improve the bill if it comes over to the Senate," her spokesperson said.
Aides for the other holdout Senate Republicans have not yet returned ABC News' request for comment.