The Trump administration - increasingly blamed by Americans for the shutdown - is trying to thread a needle between those hard-liners and Democrats who adamantly oppose spending the $5.7 billion Trump wants for a wall. "Third, I am ready to sit down at any time after the government is opened and work to resolve all outstanding issues", Durbin said.
"I am here to break the logjam and provide Congress with a path forward to end the government shutdown and solve the crisis on our southern border".
Schumer further accused the USA president of "putting forward one-sided and ineffective remedies", adding, "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".
Some 300,000 people holding visas under Temporary Protection Status (TPS) would also get three years' protection.
She said the proposals were "a non-starter" and "a compilation of several previously rejected initiatives, each of which is unacceptable and in total do not represent a good faith effort to restore certainty to people's lives".
While suggestions of "major" announcements can be overblown, Trump's comments follow a New York Times report that Democrats have added more than $1 billion to their previous offer of $1.3 billion for new border security - one of the first signs of possible movement after weeks of rancor between the president and opposition Democrats. Mark Warner of Virginia, one of the more centrist and bipartisan Democrats, declared on "Meet the Press" that the Trump offer was only a "starting point" and that Democrats would not reward "hostage taking", meaning the shutdown.
Pelosi, on Twitter, shot back at Trump. "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". But it's drawn nothing but negative reviews from Democrats so far.
It's a turnaround from Senator McConnel's previous statement that no vote should be held in the Senate until Mr Trump and Democrats agreed on a bill.
In his new proposal, Trump said he was willing to compromise by offering a three-year "provisional status" to 700,000 young illegal immigrants brought into the United States by their parents - the so-called "Dreamers".
Yesterday, he also appeared to threaten to target millions of people living in the country illegally if he doesn't eventually get his way, writing that, "there will be no big push to remove the 11,000,000 plus people who are here illegally-but be careful Nancy!"
Trump, now halfway through his four-year White House term, offered his plan to end the longest government closure in American history in a speech Saturday. She is so petrified of the "lefties" in her party that she has lost control.
Declaring an emergency would be an attempt by Trump to circumvent Congress and its power over the federal purse strings to pay for his wall.
US Democrats have gone up in arms over President Donald Trump's proposal to fund his border wall in exchange for protection for DACA recipients and TPS immigrants, denouncing it as a one-sided non-starter. His proposal would have also offered protections for individuals from specified nations who had previously been allowed to legally stay in the United States under the Temporary Protected Status program.
That partial shutdown has meant that 800,000 federal workers were either furloughed or working without pay since December 22.
The Senate Majority Leader's move to bring a bill comes days after he repeatedly obstructed House-passed bills that would have ended the shutdown.
"The notion that we have come from a (focus on a) wall to some other thing is moving it along", he told ABC's "This Week", "but we have to sit down and talk". "It is a 3 year extension of DACA", Trump said in another tweet, referring to former president Barack Obama's program to shield undocumented immigrants who entered the country as children.