Washington (CNN) With Washington just hours away from a partial government shutdown, lawmakers and President Donald Trump still have not yet reached a deal to stave off a shutdown.

An effort to broker an agreement that would prevent a shuttering of key federal agencies appears to be underway, however. Republican Tennessee Republican Sen. Bob Corker said on the Senate floor late in the day Friday that an "understanding has been reached" that the Senate will not take any further votes related to the funding issue "until a global agreement has been reached between the President" and congressional leaders.

It is not yet clear whether that effort will succeed in stopping a partial shutdown or exactly what it might involve.

Corker made his remarks just after the Senate approved a motion to proceed to consideration of a House-passed spending bill that includes an additional $5 billion for the President's border wall, and which has been widely considered dead on arrival in the upper chamber.

Vice President Mike Pence, budget director Mick Mulvaney and Trump's son-in-law, Jared Kushner, were on Capitol Hill on Friday afternoon meeting with senators, including Senate Minority Leader Chuck Schumer, a New York Democrat, about finding a solution.

The President has repeatedly said he is unwilling to accept anything less than $5 billion for his long-promised border wall. But the fact that the $5 billion border wall is viewed as a measure that would be impossible to pass in the Senate indicates that votes aren't there on the Hill to meet the President's demand.

Funding for roughly a quarter of the federal government expires at midnight, including appropriations for the Department of Homeland Security, the Department of Justice, the Department of Housing and Urban Development and other parts of the government.

Trump predicts shutdown after meeting with Republican senators

Trump predicted there likely will be a government shutdown Friday night and put the onus on Democrats -- a reversal from his position just a week ago, when he said he would "take the mantle" and not blame the opposing party.

"The chances are probably very good" that there is a shutdown, Trump said to reporters Friday afternoon while at a White House bill signing on bipartisan legislation overhauling the nation's sentencing laws.

"It's really the Democrat shutdown, because we've done our thing," Trump continued. "Now it's up to the Democrats as to whether we have a shutdown tonight. I hope we don't, but we're totally prepared for a very long shutdown."

Just a week ago, the President -- sitting in the Oval Office with House Minority Leader Nancy Pelosi and Senate Minority Leader Chuck Schumer -- said he would be "proud" to shut down the government over border security.

"I will take the mantle," Trump said last week. "I will be the one to shut it down. I'm not going to blame you for it."

Earlier Friday, Trump hosted Senate Republicans to the White House on Friday morning for discussions about the looming shutdown threat, though it was not apparent if any progress had been made during that meeting. Senate Majority Leader McConnell, upon returning to Capitol Hill from his meeting in the White House, said GOP Senators had a "good conversation" with Trump and that "we are going to continue to be talking about a way forward".

To add insult to injury: As Senate Republicans headed to the White House, a source who asked not to be identified told CNN that "things are so chaotic at the White House that some Republican senators can't get in because Secret Service didn't even have time to clear them (or the staff who is driving them there!)"

Here are the dynamics -- and the reality

House Democratic leaders have no political incentive to move and agree to a single cent more in border security money. They're even stronger in their position because the Senate has passed, unanimously, a bill to fund the government through February 8.

Trump has decided, with a major, major push from House Republican allies and conservative media commentators, that he's willing to push this fight over the edge and straight into shutdown. And he's not exactly being subtle about it.

Shutdown today if Democrats do not vote for Border Security! — Donald J. Trump (@realDonaldTrump) December 21, 2018

McConnell has attempted to give the President room to find his way out of this in every way possible. He's put his solution on the table -- and passed it through the Senate. He's more or less on the sidelines now.

House Republican leaders, as they demonstrated Thursday, are completely at the mercy of the President's position here. To think, in a closed-door conference meeting Thursday morning, they were advocating their conference get behind the Senate-passed bill. By the afternoon, after meeting with the President, it was a complete non-starter.

Anything can happen on Capitol Hill, and much more complicated deals have been crafted in less than a day before, but given the above dynamics, as one senior GOP official put it to me Friday morning: "Get ready for a long shutdown."

The President's Twitter account

JUST WATCHED Blitzer to Stephen Miller: Why did Trump fail? Replay More Videos ... MUST WATCH Blitzer to Stephen Miller: Why did Trump fail? 01:27

It may sound odd to someone outside of Capitol Hill, but you can't overstate the importance of the President's tweets to a sizable chunk of the House Republican conference. There are members who quite literally spend portions of their time trying to figure out how to garner a tweet. There are others who live in terror of a tweet. Leadership knows a single tweet can change the trajectory of a strategy or closed-door conference meeting. Even House Republicans who lost in November -- and have spoken in opposition to the President -- acknowledge the power.

"It's everything to our guys," one GOP House member told CNN on Thursday night. "It's kind of embarrassing when you think about it, but it's not a vanity thing -- it really matters that much back home in the districts."

So with that in mind, tweets like this from the President make the House GOP move Thursday completely worth it to the members, even if it leads to a shutdown:

"No matter what happens today in the Senate, Republican House Members should be very proud of themselves. They flew back to Washington from all parts of the World in order to vote for Border Security and the Wall. Not one Democrat voted yes, and we won big. I am very proud of you!"

No matter what happens today in the Senate, Republican House Members should be very proud of themselves. They flew back to Washington from all parts of the World in order to vote for Border Security and the Wall. Not one Democrat voted yes, and we won big. I am very proud of you! — Donald J. Trump (@realDonaldTrump) December 21, 2018

What happened in the House

Credit where it is due: House GOP leaders for more than a week claimed they could rally the votes for the President's wall funding plan, even as many were quite skeptical of that fact -- most notably Democratic Leader Nancy Pelosi in the Oval Office last week.

The House, 217-185, passed a bill to keep the government open until February 8 that included $5 billion in border wall funding and just shy of $8 billion in disaster relief funding. GOP leaders only lost eight Republicans. That's a big show of unity for a fractured, frustrated and soon-to-be-relegated-to-the-minority group.

The biggest question here, given the fact everyone involved knows the bill has no future in the US Senate: why not do this last week when there was cushion for a back-and-forth of competing plans with the Senate?

In the words of one Senate GOP aide: "Malpractice."

How it traditionally works

Once the House bill fails in the Senate, both parties in both chambers sit down, acknowledge what has failed and try to track a path forward. Those talks -- even in the preliminary stage -- haven't started at all yet, and given how entrenched both sides are at the moment, it's unclear when or if they will.

Staff will try to figure something out -- that's their job, and they always have options. Reality here is you can have a thousand different options, and none of them matter if the leaders aren't willing to move.

House lawmakers have been told to be prepared for further votes on Friday, but up to this point, no caucus or conference meetings have been scheduled, so everyone is basically in wait-and-see mode at this point.

Expect more legislative action in both chambers, but whether it will just be for show or for an actual solution remains an open question.

Not a great sign.

Should the government shut down, most lawmakers I've spoken to say they plan to go home for the holidays anyway and just be prepared to come back if any kind of compromise is reached. That's a problem for two reasons:

They don't see a quick resolution to this fight. It's often lawmakers being bored and tired of staying in town that helps lead to a resolution of these things.

Department of things that won't happen

Trump, following comments from a few Republican senators, tweeted Friday morning that McConnell should move to change the Senate rules to require just a simple majority to move forward on legislation (the so-called "nuclear option" to end the 60-vote threshold).

To make this as clear as humanly possible: This will never happen as long as McConnell is leader. Period. He's explicitly said as much more than a dozen times on the record that I can remember on my own. Probably more than that. It's just not a real thing. Don't treat it as such.

This story has been updated with additional developments on Friday.