Many want to see changes, still more think the price tag is far too high and all of it is pointing to a major, uphill slog as the party attempts to craft a possible compromise with Democrats -- this as millions of Americans lose crucial benefits in the face of inaction in Washington.
"It's a mess. I can't figure out what this bill's about. ...This is not going to be the bill. They're going to go negotiate with (House Speaker Nancy) Pelosi. We have no idea what the final bill will be, and we'll be the last to know," said Sen. Josh Hawley, R-Mo.
Sen. John Kennedy, R-La., said that while there is agreement about helping people with unemployment, it's the level of help where they disagree.
"At the moment we seem to have unity in disagreement. That's the bad news," he said. "The good news is -- how can I put this -- where, for the most part, we're gnawing on the same bone. We're just gnawing on different ends of the bone, but at least it's the same bone."
"We don't have any money in Washington. There's no rainy day account, no savings account," said Sen. Rand Paul, R-Ky. "So I'm not for borrowing another trillion dollars. That's an illusion of wealth, not real wealth."
"I think if Mitch (McConnell) can get half the conference that'd be quite an accomplishment," said Sen. Lindsey Graham, R-S.C.
But there is also a growing contingent in the party who fear that if enough Republicans do not get on board with a GOP product, Democrats will have an even greater chance at steering the final bill closer to the $3 trillion package passed in the House some two months ago.
"If it's passed with mainly Democratic votes, obviously they're going to have a disproportionate influence on what's in it," said Sen. John Cornyn, R-Texas, who introduced the liability protection portion of the GOP bill, saying that the final price tag is up for debate.
"I think the amount of money is still up in the air. I still think there's a need. But I'm hearing from my constituents -- whether it's my mayors, county judges, or hospitals that have had to defer elective surgery so that they are in significant financial strain or just individuals who have not been able to get back to work. I think there's definitely a need. But the amount I think is subject to debate," said Cornyn.
As for deficit concerns -- something a number of Republicans have cited -- Cornyn pushed back, saying that Republicans consulted former President George W. Bush Treasury Secretary Hank Paulson before the first $3 trillion coronavirus relief bill passed in March, and they were told that now is not the time to pull back on spending.
"(Paulson) said this is different from the structural problems we're having with the entitlements and that he would expect if we make that investment, that would help make the economy come back and in the long run be a positive thing," Cornyn told reporters.
Amid all of the disagreement, Republicans seemed united on one thing in particular -- stripping out an Administration request for $1.8 billion for a new FBI headquarters on the current site across from the Trump Hotel in Washington.
"When we get to the end of the process, I would hope all of the non-COVID related measures were out no matter what bills they were in at the start," Senate Majority Leader Mitch McConnell, R-Ky., said Tuesday after a lunch with top administration negotiators, White House Chief of Staff Mark Meadows and Treasury Secretary Steven Mnuchin.
Graham, who chairs the Judiciary Committee, which oversees the FBI, was asked why the money was in the bill.
"I don't know. That makes no sense to me," he said.
Graham told ABC News that he would support stripping the funding out of the bill.
"Even if the White House wanted it, I'd be against it because it's certainly not necessary," Sen. Mike Braun, R-Ind., told reporters.
Meadows was also asked about why the FBI construction money was included in a virus crisis funding bill.
"Well, it's just a pressing need so whether it's this bill or CR later. It's just a pressing need," said Meadows.
When pressed about why it was in this bill, he added, "You know there are a number of things in the last bill that had nothing to do with the coronavirus. I think everybody acknowledges that it's a funding mechanism. And I don't see it standing in the way of us getting a deal."
Republicans also pushed back on a pitch by Meadows and Mnuchin to consider passing stimulus bills using a piecemeal approach.
"I don't hear any support for that," Cornyn said, "I mean I've heard people float it, but I haven't heard any support for that."
And when a reporter suggested the proposal came from the White House negotiators, Cornyn said flatly, "People who are not in Congress."
A small handful of GOP senators did signal their possible support for the bill.
Sen. Lisa Murkowski, R-Alaska, highlighted that of the $105 billion in funding for schools, two-thirds of it would be given to those schools that reopen.
"Well, I think there's some important components. I'm really focused on making sure that we've got sufficient support for the schools to get our kids, not only back in, but make sure that the schools can stay open," she said.
With Republicans far from agreement, Mnuchin and Meadows are -- for now -- the GOP representatives at the negotiating table with Democrats, who have panned the $1 trillion GOP plan as stingy and missing key priorities.
Asked if it would help to have McConnell join the negotiations, Mnuchin said, "We're shuttling back and forth. It's an effective way to do it."
Meadows added, "We obviously have conversations with Sen McConnell and his people on a daily basis."
Sen. Lamar Alexander, R-Tenn., a McConnell ally and key author of the $105 billion in school funding, told reporters, "Well, I think Mark Meadows and Secretary Mnuchin need to sit down with the Democratic leaders. We now have a Republican proposal. The House has passed their bill. There's some obvious areas of agreement, like the amount of money that we have for schools -- $105 billion -- is just a little more than the House-passed bill, so maybe there's an area of agreement there. So I think step one is for Meadows and Mnuchin to sit down with the Democratic leaders and to see if there are some areas of agreement. And off we go."
The administration officials sat down Tuesday evening with House Speaker Nancy Pelosi, D-Calif., and her Senate counterpart, Chuck Schumer of New York.
Schumer who earlier in the day called the Republican Party "un-unified, unserious and completely unsatisfactory," chided his GOP colleague for not joining the meeting.
"McConnell doesn't want to be at these meetings I guess because his caucus is so divided but we're going to meet and continue to work," Schumer said.
Following the meeting, which lasted just over an hour, neither party seemed satisfied with the state of negotiations.
"It seems to me that Sen. McConnell really doesn't want to get an agreement made," Pelosi said, noting that she'll meet again Wednesday with the administration officials.
Meadows was equally pessimistic about persuading Democrats.
"I don't know that I would characterize it as getting closer," Meadows said.