(CNN) America could be sliding toward a new government shutdown and President Donald Trump may face a fateful choice over his border wall as another knife-edge week opens in Washington.

Democratic and Republican negotiators last week seemed to be on course for a deal to fund the government and boost border security short of paying for a wall, and it seemed possible that Trump might grudgingly sign on.

But the talks ground to a halt over the weekend in a dispute over limits demanded by Democrats on the number of places available in detention centers used by Immigration and Customs Enforcement operations away from border areas.

The disagreement appeared to dash hopes that a deal could be reached by Monday to allow each chamber of Congress plenty of time to pass legislation well before a Friday deadline.

"I think the talks are stalled right now," said Alabama Sen. Richard Shelby, the top Republican on the 17-member conference committee on "Fox News Sunday."

If no deal is reached and no stop-gap spending measure emerges, a new government shutdown could be triggered, again subjecting 800,000 federal workers who could be furloughed or asked to work without pay.

The most recent shutdown, which was the longest in history, ended last month in victory for Democratic House Speaker Nancy Pelosi — who refused to fund the wall — and with a damaging political defeat for the President in their first significant clash since the midterm elections.

The unpredictable Trump could rattle the effort to avoid a second shutdown when he heads to El Paso, Texas, on Monday for his first political rally of the year -- a context which seems unlikely to see him offer flexibility on the notion of building a wall.

Sudden pessimism over the conference talks between Democrats and Republicans in the Senate reflected the uncertainty and raw political nerves on Capitol Hill at the dawn of a new era of divided government.

It also reflected the excruciatingly tough task of seeking compromise on immigration policy, an issue with visceral power for both parties and which is almost an existential issue for the presidency of Trump.

Even if it turns out that the weekend's hiccup is just a typical Capitol Hill delay en route to a deal, it could precipitate even more uncertainty, since the compromise is certain to fall short of $5.7 billion in money Trump has demanded for his wall.

In that scenario, Trump would again face a choice between climbing down on the central issue of his 2016 campaign and alienating grassroots supporters and conservative pundits or refusing to sign a bill passed by Congress.

If he digs in, the President could spark a new partial shutdown for which he would again risk being blamed.

Trump's dilemma

Last week, Shelby had fueled optimism for an agreement after visiting Trump to update him on the process.

But on Sunday, he was more downbeat when asked if hopes of an agreement on Monday were realistic.

"I'm not confident we're going to get there," he said on Fox.

Two senior Republican aides told CNN that the cap demanded by Democrats on internal enforcement beds would force ICE officials to make impossible decisions about which immigrants to detain.

A House Democratic aide told CNN that Republican claims that the proposal would allow "violent criminals to be released" was false.

"This cap will force the Trump administration to prioritize arresting and deporting serious criminals, not law-abiding immigrants," the statement said.

Shelby also indicated that there was no agreement yet on how much money Democrats will allow to be spent for barriers on the US-Mexico border.

House Democratic Majority leader Steny Hoyer of Maryland said on CNN on Saturday that he would be prepared to live with a deal that offered up to $2 billion for a border barrier.

But the mix of border barriers, fencing and repairing barriers that Democrats seem prepared to support falls well short of the 200-mile wall or steel fence that Trump has recently been touting to his own supporters.

The question will be if he could somehow claim that even such a partial solution fulfills his promise to build a border wall.

Such uncertainty is why it is unclear whether Trump would sign on to a deal that emerges from the Capitol Hill talks, especially since he has balked about a solution that could get him into hot water on his right flank before.

It's also why a shutdown, once seen as highly unlikely given the political damage it wrought upon the White House last time around, cannot be ruled out.

Acting White House Chief of Staff Mick Mulvaney appears to have little more insight into what might happen this week than anyone else.

"You asked me a question: is the shutdown entirely off the table? I would say no," Mulvaney said on NBC's "Meet the Press."

So it's quite possible that Trump could find himself in exactly the same, vulnerable political position that he did during the previous shutdown.

Does he refuse to budge on funding for his wall — that represents an almost mythical symbol of his appeal to his most loyal supporters — and initiate a shutdown that would likely be opposed by a majority of Americans?

Or does he keep faith with his base and risk the ire of many other voters who are furious at government dysfunction and have told pollsters they oppose a shutdown brought on by the President to get his wall?

Trying to shift the blame

Trump seemed to be looking for a way out of his box on Sunday by trying to position Democrats to take the blame for any new shutdown.

"I don't think the Dems on the Border Committee are being allowed by their leaders to make a deal. They are offering very little money for the desperately needed Border Wall & now, out of the blue, want a cap on convicted violent felons to be held in detention!" Trump tweeted.

"Now, with the terrible offers being made by them to the Border Committee, I actually believe they want a Shutdown. They want a new subject!" Trump wrote on Twitter.

I don't think the Dems on the Border Committee are being allowed by their leaders to make a deal. They are offering very little money for the desperately needed Border Wall & now, out of the blue, want a cap on convicted violent felons to be held in detention! — Donald J. Trump (@realDonaldTrump) February 10, 2019

It was a very bad week for the Democrats, with the GREAT economic numbers, The Virginia disaster and the State of the Union address. Now, with the terrible offers being made by them to the Border Committee, I actually believe they want a Shutdown. They want a new subject! — Donald J. Trump (@realDonaldTrump) February 10, 2019

The weekend's developments still leave Trump in a delicate spot.

There's little appetite among many Capitol Hill Republicans for a repeat of the 35-day shutdown that started before Christmas and stretched into the new era of Democratic control of the House of Representatives.

There is also discomfort among some Senate Republicans over Trump's alternative plan — a declaration of national emergency that could allow the President to reprogram financing from other projects in the Pentagon.

Such a move would open the possibility that a future Democratic President could use the precedent to declare a national emergency to bypass Congress to exert executive power on another issue — combating global warming for instance.

And even if Trump does declare a national emergency, he would likely face an immediate court challenge and the most consequential constitutional showdown in an administration that has frequently tested presidential norms.

The sudden stalling of the conference committee talks at the weekend led some Democrats to consider a backstop plan.

Two sources involved in the talks said that if the impasse drags on, House Democrats may move a package that would fund the Department of Homeland Security through September along with some other departments.

That path would provoke another dilemma since it would presumably force Senate Majority leader Mitch McConnell of Kentucky to consider whether to take up a bill that the President might be unlikely to sign if it lacked wall funding.

In the last shutdown, McConnell, seeking to avoid a damaging public split in the GOP caucus, declined to expose his senators to votes on any measure that was not agreed to in advance by Democrats and Republicans.

Nothing is clear. No key player in the drama can be sure what their opponent will do next. The stakes are rising and the clock is ticking down into yet another crucial deadline on Friday.