Washington (CNN) Democrats haven't coalesced around a single proposal. Bipartisan moderates haven't either. And Republican leadership is cutting down the timeline for debate.

For those who viewed the Senate as the best chance for a resolution on the contentious immigration issue, things aren't off to a promising start.

Are there any proposals out there that can get 60 votes: Not yet.

What's on the table now: The Senate Republican proposal that turns President Donald Trump's "four pillars" plan into legislative language. It can't get 60 votes, according to aides on both sides, but it is a GOP proposal, which, as several Republican senators noted Monday, was one more proposal on the table than Democrats had laid down to this point.

Big name supporter

Senate Majority Leader Mitch McConnell said he supported the plan Monday. This isn't a huge surprise -- McConnell had made clear he supported the President's four pillars. Does it mean anything? Not really. The baseline remains the same: if it doesn't get 60 votes, it doesn't fly. But having the majority leader on board doesn't hurt.

So where is McConnell on this process?

Nobody thinks McConnell cares all that deeply about immigration policy -- in fact, it's been the source of frustration for his agenda and ideological goals for years. But McConnell also knows this is something that has to be addressed -- or at least attempted, aides say. So he has opened it up on the floor.

But don't ever assume McConnell doesn't have an idea of how this is all going to end. He wrote a book titled "The Long Game" for a reason. He knows the issue -- and its seemingly intractable position inside the US Congress, and he knows his chamber. He'll give things a chance to get 60 votes. But if it doesn't come to be, don't think he won't hesitate to call it a day and move on. There are an awful lot of judicial nominations he's got in the queue that he wants to move.

Where are Democrats right now?

Trying desperately to find a path to 60 votes.

They've held off on messaging amendments -- or even just a clean DREAM Act vote they know would fail -- in order to try and find a real path forward to 60 votes. So far, that hasn't come to pass yet.

What to keep an eye on: Messaging amendments. Before any real policy votes take place, aides say expect a series of messaging amendments (think sanctuary cities, Messaging amendments. Before any real policy votes take place, aides say expect a series of messaging amendments (think sanctuary cities, Kate's Law , etc.) While an open floor debate presents real opportunity for a solution, it also presents real opportunity for the respective party committees to get 2018ers on the board in very, very tough votes. That will almost certainly happen.

What's coming Tuesday

Sen. Jeff Flake, an Arizona Republican who's not seeking re-election, will introduce a wide-ranging amendment -- it essentially tries to find a sweet spot between his draft bill with the "Group of Six" bipartisan plan and Trump's proposal.

Key elements:

$25 billion border security trust fund for the wall

Pathway to citizenship for 1.8 million

Eliminate diversity visa lottery and reallocate visas to employment based visas and the family-sponsored migration backlog

Limit family based visas to spouses and children, and reallocate the remaining visas, to the current level, to the backlog of family sponsored immigrants, then the remaining amount split between EB2 and EB3 visas.

Will Flake's proposal fly?

It's probably too far in the family migration side for any Democrats to sign on, at least at this point, but it has a very key element -- unlike Trump's proposal, which would limit legal immigration by as much as 50%, this would maintain the current legal levels. This has been whispered about for a few weeks as the most likely potential pathway to get real Republican support and pick off Democrats. Doesn't sound like that time is ripe yet, but keep an eye one it.

Also keep an eye on: Flake has a more bare bones proposal -- maintain protections for those under the expiring Deferred Action for Childhood Arrivals program for three years in exchange for three years of border money. Democrats aren't ready to entertain that yet, but if things look to be stuck, something like that is always a possible fallback.

What else is out there: Everyone's waiting for what, if anything, the bipartisan moderate group can produce. Multiple senators continue to claim something is coming, but isn't ready yet. Pretty tough to turn something "that isn't ready yet" around for floor consideration in a matter of days.

A tight timeline

As recently as late last week, senior Republican aides were predicting the immigration floor debate could last multiple weeks -- for a fulsome debate with any number of amendments, it only made sense that it would take more than a single week. That's no longer the case, at least according to GOP leaders and aides on Monday night.

The background here: throughout the day, behind the scenes Republican leaders grew increasingly frustrated that Democrats didn't have their amendments ready to introduce Monday. At a closed-door leadership meeting, several senators raised the possibility that Democrats were just trying to drag out the debate, and a firm timeline needed to be placed on them to force action, according to two sources.

"They've been beating us up on this issue for weeks, and now that we've given them the debate they asked for, they don't have anything ready to go," one frustrated Republican aide said. "Ridiculous."

So, will this all be done by Friday? That's an awfully tight turnaround. This is as much a negotiating play by Republicans as it is a drop dead deadline. But it's clear GOP leaders want to see action soon.

Tuesday morning, McConnell didn't rule out going beyond this week but makes clear he wants it done this week.

"Senator have had plenty of time to prepare," the Kentucky Republican said. "There's no reason why we should not reach a bipartisan solution this week."