"At the moment it looks like everything has stalled out," Thune said. "So we'll see where it goes from here, if there's a will to kind of put it together and see if there's a path forward."
Trump, after initially backing the plan to restore Obamacare cost-sharing reduction payments for two years in exchange for more state flexibility, opposed the measure Wednesday.
"I think the President's view, which is most of our view, is that we need a repeal and replace plan for Obamacare. But we haven't had the votes, we haven't had 50 votes for that yet," Thune said. "So this was sort of a bridge to that I think and something that would deal with the near term need for stability in the market. But if the President is not on board with it, then it's hard to feature how it gets enough Republicans to pass in the Senate."
Senate finance committee Chairman Orrin Hatch, R-Utah, said he opposes the deal.
"That's not a way of solving our health care problem. That's a way of getting in deeper and spending a lot of money. We have to face those problems. We can't face them by continually patching billions of dollars that just go down the drain."
Both Republicans met with Trump Wednesday at the White House to discuss tax reform. Hatch said the meeting was productive and a chance for the President to hear from Democrats.
"The President was very open and very kind and spoke with the Democrats more than he did with the Republicans," Hatch said And made it very clear that he'd like to work with them."
Hatch said he think there's a chance for a bipartisan markup, that Democrats "seem to be open" to that.
Thune described the tax meeting as a "very kumbaya" moment.
"His message was to Democrats that he hopes that we can figure out something that will attract their ultimate votes when it comes time to pass the bill," Thune said.
Thune noted that the Democrats at the meeting today had signed a letter essentially saying that any tax reform bill that they could support could not include dynamic scoring
"I think they'll have to back off of that if they are going to be able to be for it," Thune said, "I felt like there was an openness to it."
"But for the Democrats to come to the table, I think they are going to have to back off this requirement or this demand they've had in their letter that there would be no dynamic scoring. Because the bill we're obviously going to put forward in order to get the economic growth that we want to get out of it, to get the rates down at where we think they need to go, we're going to assume a small amount of dynamic scoring."