Trump vowed during his State of the Union address last week to "extend an open hand" to both parties in pursuing an immigration deal that shields 1.8 million undocumented migrants from deportation.
But his proposal has been savaged by opposition Democrats, and Trump's "open hand" soon wagged an accusatory finger.
"They Resist, Blame, Complain and Obstruct - and do nothing" to break the immigration stalemate, Trump tweeted a few days after his January 30 speech.
Congress has also been haggling over spending caps for domestic programmes and the military as they seek to finalise a budget for the remainder of 2018.
But Republican leaders have acknowledged they will not meet a Thursday deadline for a spending bill, and will have to pass yet another stopgap measure this week -- with help from Democrats -- to avoid a government shutdown.
House Speaker Paul Ryan said that while both sides were "making progress" on a budget agreement, a temporary spending bill was necessary to keep the lights on in Washington.
"We're still negotiating the contents and the duration of that," he said.
Lawmakers are smarting from an embarrassing three-day shutdown last month, when Democrats refused to back a spending measure that did not break the immigration impasse.
Senate Majority Leader Mitch McConnell said this time he did not expect another threat of a government shutdown, which Trump critics blamed on Republicans but McConnell pinned on Democrats.
"There's no education in the second kick of a mule," the Kentucky lawmaker said.
Debt ceiling limit looms
Complicating the legislative schedule, Treasury Secretary Steven Mnuchin has warned Congress that the Treasury has enough cash to pay its bills only through February 28 without hitting the debt limit and using extraordinary measures to keep payments flowing.
That is earlier than expected, the Congressional Budget Office said, because last year's $1.5 trillion tax cut is resulting in less federal revenue.
Raising the debt ceiling has led to high-risk political showdowns in recent years.
With the national debt exceeding $20 trillion, some fiscal conservatives have signalled they may demand spending cuts in order to vote to raise the limit.
The crammed to-do list is further jeopardized by the partisan feuding gripping Washington over an explosive Republican memorandum that Trump declassified on Friday.
House Intelligence Committee chairman Devin Nunes argues in the document that the FBI engaged in abuse of power by relying on unsubstantiated evidence to track a Trump campaign aide.
Against this toxic backdrop, lawmakers are bracing for a heavyweight brawl on immigration.
Last September, Trump decided to end the Obama-era program known as Deferred Action for Childhood Arrivals (DACA) on March 5, meaning that the beneficiaries, called "Dreamers," could face deportation if Congress fails to act.
Last week, he unveiled a proposal that put Democrats in a bind. It would place 1.8 million immigrants, including some 700,000 Dreamers, on a pathway to citizenship -- a top priority for the opposition.
But it would also require improving border security including $25 billion for Trump's border wall, ending the green-card visa lottery, and curtailing the family reunification procedure that prioritizes relatives of US citizens immigrating to the country.
Democrats equated the plan with holding Dreamers "hostage" in exchange for anti-immigrant policies.
"Make no mistake, this plan is a complete nonstarter," insisted Senator Kamala Harris.
Trump warned Democrats they would be making a mistake if they choose to block his "generous" proposal.
"We'll either have something that's fair and equitable and good and secure, or we're going to have nothing at all," he told Republican lawmakers at their winter retreat.
On Sunday, senior Democratic Senator Dick Durbin said he did not believe a shutdown would happen, but reminded McConnell that he pledged to bring the immigration issue to the floor for debate.
"That's what we were looking for when there was a shutdown. We have achieved that goal. We're moving forward," Durbin told CNN.
Trump has received pushback from his own party.
Some hardcore conservatives have faulted him for ceding too much on immigrant legalisation.
"Illegals have No Right to be here," congressman Steve King tweeted. "This #Amnesty deal negotiates away American Sovereignty."
But moderate Senate Republican Jeff Flake, a Trump critic, warned against "drastically cutting legal and necessary immigration flows," saying Congress should not "shoehorn" the complex issue into a DACA fix.