There is little room for Republican defections in the Senate, where the party only holds a two-seat majority. On Thursday, Sen. Ron Johnson, R-Wis., told CNBC he would not vote for the measure in its current form. He said he wants to fix it so that he can support it.
Meanwhile, GOP Sens. Susan Collins of Maine, Bob Corker of Tennessee and John McCain of Arizona have voiced concern. They have not said whether they would ultimately vote for the bill.
"If you start seeing more people talk about defecting as Republicans it gets really hard to figure out how this gets put together in the Senate," Fagen said.
However, she said the "psychology of winning" the vote on Thursday was very important.
Fagen also said Senate leadership will work things out with Johnson because they can't afford to lose him.
David Bahnsen, chief investment officer at HighTower Advisors Bahnsen Group, agrees.
"Senator Johnson is not going to get everything he wants. But I think he's going to get enough to get him on board and probably improve the bill in the meantime," he said in an interview with "Closing Bell."
If the Senate passes its bill, the two chambers will have to craft a joint plan before Congress can pass final legislation.
Terry Haines, senior political strategist at Evercore ISI, said the chances of tax reform's ultimate success is pretty high.
"There's going to be a little bit of horse-trading that goes on but fundamentally what this is about is holding onto structure of aggressive corporate tax cuts, the individual tax cuts … and keeping it within budgetary lines of this small static increase in deficit that's been agreed to by the House and the Senate," he told "Closing Bell."
— CNBC's Berkeley Lovelace and Jacob Pramuk contributed to this report.