Washington (CNN) President Donald Trump's political plight gets worse with every day that passes in history's longest government shutdown .

Yet at a moment when a conventional president would fold a bad hand and spare the federal workers victimized by the debacle, Trump is digging ever deeper. And the most foreboding sign emerging from Capitol Hill on the 35th day of the impasse is that no one -- not his Republican allies or Democratic foes -- has any idea how he plans to extricate the nation from the darkening crisis.

Trump's lack of strategy poses a severe obstacle to nascent efforts that are finally underway among leaders on Capitol Hill to find a resolution. The President's weakening position and adamant refusal to change tack were laid bare Thursday after a failed pair of Senate votes on competing partisan measures.

But his Teflon self-confidence emerged unscathed from his loss of a significant battle in the shutdown war to House Speaker Nancy Pelosi after he admitted defeat in his demands to give his State of the Union address next Tuesday.

Even dire warnings of safety lapses in the skies, fears of worsening self-inflicted damage to the economy and a rash of tin-eared comments by rich Trump supporters did not dent the President's determination.

It's either personal resilience on Trump's part or a sign of a dangerously unchained presidency, depending on where you stand, that he does not perceive political winds shifting against him, or chooses to barge on anyway.

So with Washington waiting to see how he would climb out of a new political hole on Thursday, the President just doubled down on the same basic position that Democrats have repeatedly rejected.

For weeks, he's been saying the government cannot reopen until he gets money for his border wall. Now he's ready for the government to reopen for a few weeks -- but only if he gets money for his border wall.

Trump said that if Senate Majority Leader Mitch McConnell and Senate Minority Leader Chuck Schumer come up with a "reasonable" deal in tentative talks, he would be open to it. But with one condition -- "a prorated down payment for the wall."

Trump delivered his offer in a whirling session with reporters that was at times difficult to follow but included a trademark warning that undocumented border-crossers "permeate" the nation, as far as Wisconsin.

What does the President want?

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One conventional endgame would be for Democrats and Republicans on Capitol Hill to call a halt to hostilities and freeze their rival positions in a compromise that both sides dislike but can stomach. Democrats could say they offered money for border security. Trump could fog the issue and say he got cash for the wall.

But even if Schumer and McConnell can reach such a point -- and get House Speaker Nancy Pelosi on board -- the President's behavior suggests it's no sure thing he could swallow a classic congressional fudge.

In fact, there is confusion as to exactly what the President plans to do next and what he would accept in a final agreement. And even when there is a deal on the table, on immigration and other key legislative matters, he has a history of changing his mind. That's how the partial shutdown started in the first place.

Asked about the "prorated" wall payment, Maryland Sen. Ben Cardin seemed mystified and replied: "I have no idea what that means."

Pelosi quipped: "I don't think he knows what he wants."

Sources told CNN's Phil Mattingly that the biggest problem remained a lack of clarity about what the President would accept in any deal to end the shutdown.

Democrats argued that a prorated payment would give the President the idea that he could just keeping shutting down the government in return for piecemeal payments for the wall.

"The principle at stake here is we cannot allow Donald Trump to use the harm of a government shutdown as a negotiating tactic," California Rep. Ted Lieu said on "The Situation Room" on CNN on Thursday.

"We cannot allow any party or any person to take our government as a hostage and extract a ransom," Lieu said.

What was remarkable was that the President seemed to take no notice of a recent deterioration of his political position in Washington.

Maybe it's iron will. Maybe Trump is characteristically creating himself a new reality that suits him better. Or perhaps he realizes his base would never forgive him if he folds on the wall, the existential epicenter of his political appeal.

A bad day in the Senate

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By any measure Trump was in a deeper hole by the end of Thursday than he was when the day dawned, but he refused to let it change his basic approach.

The President's worsening political problem was revealed in the Republican-led Senate in votes that were doomed to fail but that some lawmakers hoped would open the way to serious negotiations on Capitol Hill on a way out of the mess.

A GOP bill enshrining the President's offer to end the shutdown -- temporary protections for some undocumented immigrants in return for $5.7 billion for a border wall -- fared worse than a rival Democratic measure.

Six Republican senators crossed the aisle to vote "yes" on the Democratic bill, which would have reopened the government without giving the President any money for his wall. Their number included several senators with tough 2020 re-election fights.

Those votes and the fact that the Democrats hold the House indicate that the political gravity that will shape any way out of the shutdown -- as well as polls in which a majority of Americans blame Trump for the debacle -- now favors Democrats rather than Republicans.

But the President is refusing to see things that way.

"Look what just happened on the floor -- the idea he has leverage here is not in touch with reality," a Democratic aide told CNN's Mattingly.

As it stands Friday morning, Democrats are demanding that Trump reopen the government ahead of any talks on funding border security -- but indicating that in any case there will be no money for the wall.

The President says the government can get up and running only if Democrats fold on wall money -- even if it's a couple of hundred million dollars to tide him over while negotiations take place.

CNN exclusively reported Thursday that if Trump is finally forced to concede there is no way to get Congress to fund the wall he always said Mexico would pay for, he has a backup plan.

The White House is preparing a draft proclamation for the President to declare a national emergency along the southern border and has identified more than $7 billion in potential funds for the wall, according to internal documents viewed by CNN

Such a step would cause a political firestorm, questions about whether Trump had usurped his constitutional powers and a potential legal fight that could drag on for months. Such a scenario is one reason why the President's advisers appeared to have moved away from such a step several weeks ago.

But given the disconnect on Capitol Hill, Trump's determination not to fold and the lack of any sense about how he plans to navigate out of the shutdown, the Hail Mary of a national emergency could come back into favor.

For now, McConnell and Schumer will press ahead as informal groups of senators try to forge compromise as well.

But so far, there's no progress and still no end in sight as federal workers go without another check on Friday.

"Well, at least we're still talking," McConnell said as he left the Senate for the night.