First, they are demanding a compromise that would include extending President Barack Obama's Deferred Action for Childhood Arrivals protections for 800,000 immigrants, he said.
Hoyer said Trump himself mentioned fences and technology.
Immigration resonates deeply with both parties' bases, increasing the pressure on elected officials to deliver, but Republicans and Democrats have shown little sign of breaking that impasse. The Trump administration dissolved the program in September, granting one final two-year extension for people whose DACA permits expire by March 5, 2018. Wall funding wasn't included in a stopgap year-end funding bill, nor was it ever considered when Democrats thought they'd struck a deal on DACA with Trump this fall.
Dick Durbin of IL, the No.2 Democrat in the Senate, has criticized the request made by the administration for wall and border security spending.
"I really do believe Democrat and Republican, the people sitting in this room, really want to get something done", Trump said.
A Republican candidate has dropped out of the race to represent New Mexico in the United States House of Representatives.
"My position is going to be what the people in this room come up with", he added. Trump challenged the group to "put country before party" to get a deal done.
And the President has expanded on that demand, now including an end to so-called "chain migration" - a term that refers to the process by which immigrants can eventually bring relatives to the country, part of the U.S. immigration system's focus on family reunification - and to a diversity visa lottery that he has cast as a peril to national security.More news: Cameron Jordan pokes fun at Cam Newton after Saints' win
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"Unfortunately, following that meeting, the White House issued a series of unreasonable demands entirely outside the scope of our ongoing negotiations about DACA and border security", Schumer said on the Senate floor Monday.
"If the White House backtracks on what they said they're going to get from a DACA bill, it's going to have negative political consequences for the president", said Ruark.
Yet it seems that Trump is remarkably willing to trade a largely pointless border wall for a less stringent immigration policy than perhaps his base had expected.
Trump also said he hoped to pursue a "comprehensive" immigration bill after lawmakers strike a deal on the dreamers.
Sen. Patrick Leahy, D-Vt. suggested an "easy way out" of the stalemate. "So let's see how much money they send up and then we can decide what kind of a wall".
Separately, Senate Majority Whip John Cornyn, R-Texas, said Tuesday that another short-term spending bill to buy more time for negotiations is "likely".
The New Mexico Attorney General's Office is hoping a new disclosure form will provide more information for customers considering rooftop solar.