In a Saturday speech from the White House, Trump offered three years of protections for Dreamers and for holders of temporary protected status (TPS), another class of immigrants from designated countries affected by armed conflict, natural disaster or other strife.
The shutdown has caused widespread disruptions. But this one is the longest on record. Some 800,000 federal workers have been ordered to stay home or work without pay during the shutdown.
"She is so petrified of the "lefties" in her party that she has lost control", Trump said of the House speaker.
Senate Minority Leader Chuck Schumer echoed her stance shortly after Trump laid out the details of his plan to reopen the government, now nearly a month in shutdown.
Pointedly ignoring his personal comments, Pelosi on Twitter emphasized the need to end the impasse, which has inflicted increasing pain after one month, with some government employees having to turn to food banks or local charities to get by. But Democrats says talks on border security should occur only after the government is reopened.
But more common was the reaction of Rep. Adam B. Schiff, California Democrat, who accused the White House on Sunday of politicking.
Senate Minority Leader Chuck Schumer also panned the proposal as "more hostage taking", saying that it was Trump who had "single-handedly" imperilled the future of the immigrants he proposed to help. He called it "a good-faith compromise".
"Instead of succumbing to the president's strategy of negotiating through hostage taking, Mitch McConnell should bring the House passed bills to the floor of the Senate for a vote and end this shutdown".
Huawei probe underlines U.S. fears of China's strategic threat
The investigation is at an advanced stage, and an indictment could come soon, according to the person familiar with the matter. The Chinese company has already become a major part of the trade dispute between the USA and China .
He came up with a number of immigration proposals, seeking funding for a wall on the US-Mexico border, which he had earlier said would tackle illegal immigration-related problems, such as illegal drug smuggling, human trafficking, cartel violence, and sexual assaults.
- Three years of legal protections for so-called "Dreamers", a group of about 700,000 immigrants who entered the country illegally as children.
Democrats indicated on Sunday talk shows a willingness to fund border upgrades of some sort, but they want a permanent fix protecting Dreamers - young people brought to the USA illegally as children - and other migrants from deportation, not the three-year-reprieve offered by Trump.
Even as his proposal was rejected by Democrats, Trump also faced fire from some conservatives who derided his immigration overtures as "amnesty".
He tweeted: "No. Amnesty is not part of my offer". "The fact that he's saying three years just for DACA just shows that he's not serious".
Former Democratic President Barack Obama put DACA in place in 2012 through an executive order.
"Amnesty will be used only on a much bigger deal, whether on immigration or something else", he tweeted on Sunday, before adding a warning to Pelosi: "Likewise there will be no big push to remove the 11,000,000 plus people who are here illegally-but be careful Nancy!"
With those kinds of incentives for both sides, a deal seems likely. "We're going to work hard and reach across the aisle". Can we amend it? What we can not do, and I've actually had Republicans as well recognize this, is that we can not reward the kind of behavior of hostage taking. "Let's find a way to be able to get the government open because there are elements in this that are clearly elements that have been supported by Democrats strongly in the past".
Reacting to the cool reception, Trump fired a flurry of tweets Saturday morning lashing out at Pelosi personally. But the Secret Service and Department of Homeland Security quickly responded to Pelosi's concerns, assuring that the Capitol would be fully secured if the president were to visit. There's only way out: "open up the government, Mr. President, and then Democrats and Republicans can have a civil discussion and come up with bipartisan solutions".