Earlier this week, we listed 10 Republican senators who had potential reservations about their party’s tax policy bill — way more than the three GOP votes needed to kill it. Now, with the Senate voting on this legislation as soon as Thursday night, it looks like that opposition is falling away.

Why? On the one hand, party leaders are promising to change the bill to please many of the holdouts. On the other hand, some of the holdouts are either dropping their demands or accepting changes that have the appearance — more than the reality — of addressing their publicly stated concerns.

Montana’s Steve Daines and Wisconsin’s Ron Johnson had asked for the bill to offer more benefits to certain kinds of businesses called pass-throughs, and Senate GOP leaders are expected to allow a vote to adopt those changes later Thursday. Additionally, Alaska’s Lisa Murkowski and Arizona’s John McCain were considered wild cards simply because they voted against the GOP Obamacare repeal bill over the summer, but neither had expressed any deep reservations about the tax measure. Murkowski announced Wednesday that she indeed supports the bill, and McCain followed suit Thursday. So those four moving to the “yes” column makes sense.

Maine’s Susan Collins, wary of this bill’s inclusion of a repeal of the individual mandate of Obamacare, says party leaders have pledged to her that they will enact a separate bill, known as Alexander-Murray, that is designed to shore up the Affordable Care Act’s health marketplaces. In fact, according to Collins, party leaders say they will pass Alexander-Murray before the final vote on this tax bill, which still must go through the conference process because the House passed a different version.

That has the appearance of giving her the essential thrust of what she wants — a way to preserve the mainstays of Obamacare. But here’s the problem: The enactment of Alexander-Murray cannot be guaranteed by Senate Majority Leader Mitch McConnell. To avoid a filibuster — which can’t be used on the tax measure because Republicans are using budget reconciliation rules — Alexander-Murray requires 60 votes in the Senate. In other words, some Democrats, who have been strongly opposed to the tax bill, would have to help pass the health care bill even as they know it will ease the GOP’s tax push. Also, there is no guarantee that the House, full of conservative members who hate Obamacare and may never vote for a bill to make it work better, will agree to that provision. Finally, the Congressional Budget Office says that passage of Alexander-Murray would not meaningfully affect its prediction of the ill consequences of repealing the individual mandate: an increase in the number of Americans who are uninsured (up to 13 million) as well as an increase in the cost of insurance for some Americans with coverage.

Collins is not the only one backing the tax bill on what seems to be wishful thinking. Tennessee’s Bob Corker and Oklahoma’s James Lankford, who have complained that this legislation could increase the deficit too much, also appear to be have been placated by a gesture that is unlikely to result in their stated goal. A so-called trigger imposing automatic spending cuts or tax increases if the deficit grows too much will likely be put into the legislation on Thursday. (The proposal has not been released publicly yet.) I’m skeptical that a future Congress will actually feel bound by this trigger. But again, Corker and Lankford can back this bill and publicly say their concerns were addressed, even if they know that is probably not true.

There are still some unknowns. Arizona’s Jeff Flake and Indiana’s Todd Young also cited deficit concerns before this week, though they have not been as vocal in demanding changes as Corker and Lankford. Kansas’s Jerry Moran, who like Collins complained about the repeal of the individual mandate, has also not made a formal push this week for changes to the bill. So they remain wild cards. And if I were a Republican leader, I would be most worried about Flake because of his political freedom. (Flake is not running for re-election.)

I expect this bill to pass. Unlike in July, when Collins and Murkowski opposed even a procedural motion to take up the health care bill, all 52 Republicans on Wednesday voted to move along this tax bill. On the other hand, I expected the Obamacare repeal to pass up until the moment McCain voted no.