His plan would give $5 billion for the border wall in exchange for renewable work permits for Dreamers.
He said the President was now pushing for a steel slat structure, rather than a concrete wall.
The Democrats' position only gets stronger on Thursday, when California Democratic Rep. Nancy Pelosi is set to become the next speaker after her party picked up 40 seats and control of the House in the November midterm elections. White House officials have said Trump could be open to this idea again, though Democrats say they don't trust Trump to complete the deal without adding demands at the last minute.
"The president still says "wall" - oftentimes frankly he'll say "barrier" or 'fencing, ' now he's tended towards steel slats".
"At this point, it's clear the White House doesn't know what they want when it comes to border security", said Justin Goodman, Schumer's spokesman.
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I have to process. "My coach told me that when I hit her the first time, it would make her insane and want to come get me". And for what it's worth, the aftermath of Nunes's pulverizing victory included Cyborg sounding hungry for a rematch.
House Democrats did not confer with Senate Republicans on the package, but the bills expected to have some bipartisan support because they reflect earlier spending measures already hashed out between the parties and chambers.
"Either we build (finish) the Wall or we close the Border", Trump - who has adopted the 2020 re-election mantra "promises made, promises kept" - posted as recently as Friday. As a result, parts of the federal government, including the Department of Justice and Department of Homeland Security (DHS), shut down when their funding expired on December 21.
He tweeted: "Nancy Pelosi's newest funding proposal doesn't represent any serious attempt to secure our border or find a compromise".
The U.S. federal government entered a partial shutdown 10 days ago, after Congress failed to agree to a budget containing funding for the barrier demanded by the White House.
"It would be the height of irresponsibility and political cynicism for Senate Republicans to now reject the same legislation they have already supported", the leaders said.
Building a solid "wall" along the 2,000-mile (3,200-kilometer) US-Mexico frontier was a central plank of Trump's 2016 election campaign, and he has tweeted about it nearly 100 times this year alone.
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Trump deflected criticism on Saturday over his administration's responsibility over the two migrant deaths that took place while they were in custody of the US Border Patrol.
But Graham said there would never be a government spending deal that did not include money for a wall or other physical barriers on the southern border.
Democrats plan to put the ball back in Trump's court immediately on Thursday by passing a general spending bill which would allow the government to reopen fully, but would not include extra wall construction money, United States media reports said.
Before leaving, he gave a rare interview to the LA Times, published on Sunday, in which he called the role a "bone-crushing hard job". In January, Kelly drew Trump's ire by telling congressional Democrats the president had "evolved" on the wall and was not "fully informed" when he made it a campaign issue. Independent agencies, including the Securities and Exchange Commission, are also affected.
Mr Trump is struggling to get the funding needed to start building the wall.
Talks have been at a stalemate for more than a week, after Democrats said the White House offered to accept US$2.5 billion for border security. Gates are closed at some national parks, the government won't issue new federal flood insurance policies and in NY, the chief judge of Manhattan federal courts suspended work on civil cases involving US government lawyers, including several civil lawsuits in which Trump himself is a defendant.
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Live Nation Las Vegas president Kurt Melien went onto reveal how the hype surrounding residencies is a generally new phenomenon. After the 2018 year-end shows, the residency is spread out through 2019, from January until the beginning of November.
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