CNN  — 

The White House and Senate Republicans managed to spend the opening day of stimulus negotiations at odds not with Democrats, but with one another.

A final GOP proposal expected to sit around $1 trillion, which senators expected to be unveiled by mid-week, has several major holes and unfinished pieces, according to people directly involved. It has been, to say the least, an inauspicious start to a three-week sprint to lock in the second largest economic rescue package in US history.

Bottom line: Republican senators know they need to figure things out quickly, expect they will and Tuesday is a crucial day to taking that step. Treasury Secretary Steven Mnuchin and Mark Meadows, the White House chief of staff, held three significant meetings on Capitol Hill to try and pull things onto some semblance of a negotiating path.

“We’ll get it together,” one GOP senator told CNN on Monday night. “Sometimes it takes some time to get everyone on the same page.”

Of note: There’s a reason Senate Majority Leader Mitch McConnell didn’t move quickly on a second major stimulus proposal – his conference wasn’t on board. The disputes between Republicans and the White House are just the surface of some major underlying tensions among GOP senators that are likely to come to the forefront in the days ahead, aides tell CNN. The pitch will be, according to two GOP senators supportive of the forthcoming proposal, that unity will provide Republicans with the most leverage for the talks with Democrats. That, in the past, has been a message that moves the conference into line. But a number of Republicans are in a much different place than they were in March.

The crux of the Senate GOP disputes

The White House. Period. The issues that have caused the most heartburn among GOP senators – so much so that dozens raised concerns to reporters on Monday night – are White House priorities. The payroll tax cut has somehow become Trump’s red line of sorts during these talks, even though a decent majority of the Senate GOP is cool or outright opposed to the idea (Of note: the House GOP is on board with the payroll tax cut).

How keen on it is the President? Well beyond repeatedly threatening to veto the next stimulus package if it isn’t included during the private White House meeting with McConnell and House GOP Leader Kevin McCarthy, Trump made a point of getting conservative Arthur Laffer on speaker phone in the Oval Office to tout the merits of the proposal – and warn against limiting its scope, according to two people briefed on the meeting. (Laffer also discussed a health care price transparency proposal, the people said.)

The White House also ran into a buzz saw by proposing to zero out grant money for testing and tracing, as well as new money for the Centers for Disease Control and Prevent and the National Institute of Health on account that there is still money left in those accounts. More than two dozen GOP senators told CNN on Monday night they supported the additional funds.

The view from the Hill was best summarized by Sen. Roy Blunt of Missouri, a member of GOP leadership and the chairman of the health panel of the Appropriations Committee: “I just think that’s wrong.”

Astute quote of the day: From Sen. John Thune, the South Dakota Republican and second-ranked GOP senator, on the prospects for the payroll tax cut in any final deal:

“His advocates – Mnuchin and Meadows and others – I think will probably try and ensure that it’s at least included in the first draft.” Translation and reality check: a version of the payroll tax cut will likely be in the first GOP draft – Mnuchin said as much Monday night. But with Republicans cool to the proposal and Democrats completely opposed, a payroll tax cut has future prospects about as rosy as that of the dodo bird.

To make something clear here: These are just topline disputes between Senate Republicans and the White House. There are no shortage of very real policy disputes inside the Senate GOP conference itself that need to be ironed out. With that in mind, CNN’s Manu Raju reported last night that McConnell still hasn’t tipped his hand on what exactly is in the final legislation. Indeed, people involved say there are still open pieces being worked through and they are further away from a final draft than has been commonly assumed the last few days.

Unemployment insurance

Republicans have been clear they plan to revise, reduce and restructure the $600 federal unemployment enhancement, which expires for tens of millions of Americans at the end of the month. Mnuchin said Monday he wanted an agreement by next week so it didn’t lapse, but lawmakers and aides all agree that is exceedingly unlikely at the moment. The enhancement is supported by Democrats – the House already passed an extension of the $600 benefits – and while Democrats haven’t made it a redline item, they’ve made clear any reduction must be paired with other assistance.

Underscoring the issues the talks will face: Trump, in the private portion of the meeting with McConnell and McCarthy, ripped into the inclusion of the enhancement in first stimulus measure, according to two people familiar with the President’s comments. He criticized how it was structured and said it never should’ve made it into law in the first place.

GOP plan: More direct payments and $105 billion for schools

McConnell announced Tuesday the Republican stimulus proposal will likely include $105 billion in funding to help reopen schools across the country.

“This majority is preparing legislation that will send $105 billion, so that educators have the resources they need to safely reopen,” McConnell said in a floor speech.

In comparison, Democratic leadership has proposed $430 billion as part of their next relief package to help schools reopen.

The majority leader broadly outlined what will be in the GOP proposal of the next Covid-relief bill in a floor speech on Tuesday morning, which he said “are just some of the elements being discussed between Republicans and the administration” and will be released “very soon.”

He said it will likely include another round of direct payments to Americans and more targeted funding of the Paycheck Protection Program.

“Speaking of building on what worked in the CARES Act, we want another round of direct payments,” he continued.

The path forward

Republicans will meet to walk through the current state of the proposal during their conference lunch on Tuesday. The intention, senators said Monday night, is still to have a proposal out for public consumption later this week. Notably the path for what happens after that hasn’t been laid out yet by McConnell – underscoring that there are just a lot of unknowns right now. And unknowns, plus the extent of the intraparty policy disputes, on top of the very significant cross party disputes, means this is going to take awhile.

Where Democrats sit

The meeting between Pelosi, Schumer and the top White House negotiators will be the first substantive conversations of any kind on the next stimulus, aides say. Schumer has already made clear Democrats will oppose the looming GOP plan, but he did lay out his expectations for next steps on Monday night.

“I believe they will, even with this stingy bill, come to the table,” Schumer said. “And we will negotiate.”

This story has been updated with additional developments Tuesday.

CNN’s Ali Zaslav, Ted Barrett, Manu Raju and Lauren Fox contributed to this report.