He continued: "I said bye-bye, nothing else works".
The White House moved to pre-empt the Democrats, telling reporters Monday that tax refunds would be paid despite the shutdown.
"And he just got up and said, 'Then we have nothing to discuss, ' and he just walked out".
"I prefer that we get this resolved the old-fashioned way, " Thune said.
He claimed they could resolve the standoff in "45 minutes", but previous meetings have led to no agreement as Trump insists on the wall that was his signature promise in the 2016 presidential campaign.
"I asked what is going to happen in 30 days if I quickly open things up, are you going to approve Border Security which includes a Wall or Steel Barrier?"
With the two sides at an impasse, some 800,000 federal employees are expected to miss their first paycheck, on Friday, since the shutdown began on December 22.
"The president seems to be insensitive to that". He blamed illegal immigration for what he said was a scourge of drugs and violence in the USA and asked: "How much more American blood must we shed before Congress does its job?" Trump called the situation on the southern border as a "humanitarian crisis - a crisis of the heart and a crisis of the soul". Earlier, the president traveled to Capitol Hill to meet with Senate Republicans, saying afterward, "We have a very unified party". "There was no discussion about anything other than solidarity".
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Trump is scheduled to visit the southwest border tomorrow and it was not clear whether he still might choose to make the national emergency declaration. "Our responsibility is to do what we think is in the best interest of the American people and the effective and efficient operations of their government". "I really believe the Democrats and the Republicans are working together".
Trump stopped short of an emergency declaration in his televised speech but repeated his assertion that illegal immigrants and drugs flowing across the southern border are a serious threat to American safety.
Meanwhile, House Speaker Nancy Pelosi says the president has "chosen fear" in making the case to the American people for the border wall and Democrats "want to start with the facts".
Democrats and other opponents of a border wall had threatened to take legal action if Trump issued the order.
"I'm not optimistic that anything will change [as a result of these speeches]".
Schumer noted that Trump had promised to have Mexico pay for the wall.
Vice President Mike Pence was asked how Mr. Trump walking out of the room is productive.
McConnell blasted Schumer for holding up Senate votes on unrelated foreign policy measures during the budget impasse.
The Department of Homeland Security (DHS) said a year ago alone it encountered more than 3,000 "special interest aliens" at our southern border. "We've shown our willingness to work with them". "I think most Americans understand that it's purely political". He should let that go. Meanwhile, almost 800,000 federal employees have been furloughed.