WASHINGTON — President Donald Trump's victory in Washington's shutdown standoff could be short-lived if he doesn't also find a way to deliver a win to "Dreamers," providing legal status to people who were brought to the United States illegally as children and will face deportation in March absent a federal reprieve.

It was Trump who set a March 5 deadline by rescinding President Barack Obama's Deferred Action for Childhood Arrivals program in September, then calling on Congress to come up with a fix.

On the campaign trail, Trump promised to crack down on illegal immigration, and polls show that a significant minority of his base would prefer to deport Dreamers. But overall, according to an NBC/SurveyMonkey poll released Tuesday, two-thirds of Americans support Obama's DACA program.

And therein lies the rub: If Trump can't come to an agreement with Democrats in Congress by March 5, he'll have to decide whether to infuriate immigration hard-liners by unilaterally extending the DACA deadline or risk further energizing Democrats and alienating moderate Republicans by leaving Dreamers vulnerable to deportation.

White House press secretary Sarah Huckabee Sanders declined to say Monday whether, absent a deal, Trump would deport Dreamers.

"We haven't determined that," she said. "We're hopeful that we don't have to do that and that we don't have to get there."

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On Wednesday, Sanders said the White House would issue a "legislative framework" that provides a "permanent solution on DACA" next week, though she declined to give specifics.

But in October, Sen. James Lankford, R-Okla., said Trump had assured him privately that the deadline would be extended if no deal is reached.

"The president's comment to me was that: 'We put a six-month deadline out there. Let's work it out. If we can't get it worked out in six months, we'll give it some more time,'" Lankford said.

It's Democrats in Congress — led by Senate Minority Leader Chuck Schumer of New York — who are playing games with the fate of the Dreamers, said former Trump adviser Michael Caputo. Schumer had offered last week to support Trump's wall but later withdrew that proposal.

"By taking this new position today, Schumer is pushing the president to make an inadvisable decision on deportation of the very people who Schumer wants to save," Caputo said. "That’s a sucker’s bet and not one that the president’s going to make."

He predicted that, if no deal emerges, Trump will simply extend the deadline.

"This is a political equation that Chuck Schumer has put up on the chalkboard. All the president is going to do is take the eraser, walk up to the chalkboard and erase it," Caputo said. "The only person playing brinksmanship with these Dreamers is Chuck Schumer."

Whoever is to blame, the two sides appear to be further away from an agreement than they were on Friday when Trump and Schumer munched on cheeseburgers and tried to hammer out an accord — or when, the week before that, senators presented a centrist-oriented fix for Dreamers that Trump rejected out of hand.

Senate Majority Leader Mitch McConnell, R-Ky., has said it is his intention to let the Senate write a new immigration bill on the floor in February, but Trump and Democratic leaders have been at loggerheads over the White House's insistence that any new law include full funding for a border wall between the United States and Mexico and provisions curtailing the diversity visa lottery and family migration.

Like Trump, Republican leaders in Congress have said they want to devise a solution that gives legal protection to Dreamers, but they, too, fear a backlash from their right flank if they fail to extract significant concessions from Democrats on other immigration issues.

House conservatives have been pushing GOP leaders to allow a vote on legislation, called the Securing America's Future Act, that would achieve many of the White House's goals in tightening restrictions on both illegal and legal immigration.

Rep. Michelle Lujan Grisham, D-N.M., calls that bill the "Mass Deportation Act."

"The bill undermines local law enforcement, it hurts farmers, hurts families, guts legal immigration; and aims to rip apart communities through mass deportation, while only providing Dreamers with temporary protections and no pathway to citizenship," she said Tuesday. "This deeply partisan, anti-immigrant bill was written by a group of Republicans with no bipartisan input or support."

With House conservatives trying to drag the discussion to the right and Senate liberals, including several potential 2020 presidential candidates, having shown that they're willing to go to extremes to force action — like the government shutdown they precipitated over the weekend — no sweet spot has emerged.

And that's not surprising after more than a decade of partisan bickering, and little progress, over legislative proposals that would marry creating a legal path to citizenship for the 11 million or so immigrants who are in the country illegally with enhanced border security and new visa standards to favor bringing highly skilled workers into the United States.

Trump, who has made a habit of tossing hot-button issues to Congress, may soon find that this decision is much tougher to dodge.