(CNN) President Donald Trump sent a list of demands to Capitol Hill on Friday ahead of his White House meeting with lawmakers, releasing publicly a letter sent to members of Congress outlining the reasons why he continues to seek a border wall, to end the government shutdown, now in its second week.

"As the enclosed presentation makes clear, current funding levels, resources, and authorities are woefully inadequate to meet the scope of the problem," Trump wrote in a publicly released letter. "We are no longer in a status quo situation at the Southern Border but in a crisis situation. Status quo funding is not enough."

"Absolutely critical to border security and national security is a wall or a physical barrier that prevents entry in the first place," Trump said.

Democrats however believe they have effectively jammed Senate Majority Leader Mitch McConnell with the plan the House passed Thursday night -- a bill to reopen the government with no additional wall funding -- and that Kentucky Republican's rank-and-file senators will start to feel the pressure and start to send word that it's time to buck the President and put the Democratic proposals on the floor.

Given that, Democrats don't plan on moving off their position (the two bills passed Thursday) at least until Republican senators come back to Washington next week to face the press (and pressure). Democrats believe they not only hold the political high ground in the fight, but have also now put the policy hot potato back into the laps of the GOP, aides say. They point to Republican Sens. Cory Gardner of Colorado and Susan Collins of Maine saying the shutdown should end before a deal is reached on a wall as the prime examples of their strategy at work.

Pressure in the Senate

Democrats have wasted no time amping up their rhetorical pressure now that they've passed the bills, with House Majority Leader Steny Hoyer targeting McConnell directly.

"They are his bills. He already passed them. We are either a co-equal branch of government or we're not," Hoyer said when pushed on the fact McConnell wouldn't be bringing up the House bills. "If we are a lap dog for the President, that's unfortunate and it has resulted in shutting down the government of the United States of America. That's bad policy and, I would suggest, bad politics."

All that said, aides have made clear -- and the Senate majority leader's public comments reflect -- that McConnell is as dug in as ever not to move until Trump signs off on something. As evidence, this was McConnell on the Senate floor Friday morning before the White House meeting on the Democratic proposals:

"The package presented by the House's new Democrat leaders yesterday can only be seen as a time-wasting act of political posturing," McConnell said. "It does not carry the support of the President. In fact, the administration explicitly indicated yesterday the President would actually veto it. And it cannot earn the support of 60 of my colleagues here in the Senate."

Senior Republican aides also noted that the decision by Collins and Gardner as hardly reflective of where the broader conference stands.

It's also important to view those two senators for their current realities -- both were opposed to the shut down and the reasons for it before it occurred. Gardner was actually working behind the scenes to connect the White House to Democrats in an effort to stop it in its final hours. Both are also top 2020 targets for Democrats.

But keep in mind, even with a vastly expanded map for Republicans to defend in 2020 (including McConnell's seat), politically there are far more Republicans in states where the President still has solid approval numbers. Undercutting the President on his signature issue could carry longer repercussions than a shut down fight that most will forget about within a few weeks after its resolution. Now if several more GOP senators come out and break with the President in the days ahead, then it would signal an important shift. But for now, it's not something that will force a shift of any kind.

Democrats see Gardner and Collins as evidence their legislative strategy is working. McConnell won't move on anything until the President signs off. The President and his team have made clear a border wall has to be in any deal, and House Speaker Nancy Pelosi says there will be no wall. This is going to take more time to play out, lawmakers and aides in both parties acknowledge.

Is DACA included?

CNN is told explicitly from leadership on both sides a solution for recipients of the Deferred Action for Childhood Arrivals program is still not in play right now.

Republican Sen. Lindsey Graham of South Carolina is trying to make it a thing. It's not a thing at the moment.

Democrats have made clear they don't trust the White House or President to follow through in any broader deal and have no desire to go down that path. Republicans are keying off the President, who while aides say he didn't explicitly reject Graham's private pitch to him, has not told his team to communicate to Capitol Hill that it was in play. The battle lines remain wall vs. no wall at the moment.

That said, the longer this goes, the more time rank-and-file lawmakers have to talk/try and figure out their own organic plans. We've reported on the fact that these are occurring, but that nothing is ripe at the moment. Worth keeping an eye on in the days ahead as leaders remain so very dug in.

A final point: historically shutdowns end when the pain becomes particularly acute, either politically, or to the federal government and its workers, or both. That hasn't kicked in yet on either front. But keep an eye on the latter issue in the coming week. A large portion of the 800,000 federal workers now furloughed or working without pay will miss their first full paycheck on January 11. That's real pain. With real ramifications. And that's often the kind of thing that drives folks to the table.

So why hold a meeting on the government shutdown in the Situation Room?

There are a few reasons.

The White House message during the shutdown has been that there is a "national security emergency" at the border -- White House press secretary Sarah Sanders used these exact words this morning -- and the Situation Room lends an air of seriousness to the debate for the White House.

The Situation Room is also typically a no-press zone because it is a setting for classified intelligence, which means no opportunity for cameras or questions (although rare exceptions have been made in the past). Having no press in the room means private discussions and avoids another photo-op moment between Trump, Pelosi and Senate Minority Leader Chuck Schumer.

The invitations also didn't use the word "briefing" this time, just a meeting between principals. Because of this many on the Hill are expecting it will be just talks, but Democrats are also expecting the White House to put on some sort of show -- similar to the Homeland Security Secretary Kirstjen Nielsen briefing on Wednesday -- which was not classified and could have been held anywhere in the White House.

Bottom line: Trump likes the gravitas and air of seriousness the Situation Room brings even though it is technically just another conference room when national security and classified information is not being discussed. The Oval Office, which is traditionally used for meetings with congressional leadership, would serve the same purpose in theory.