Washington(CNN) A key reason why the White House has not agreed to a deal that would reopen the federal government is that West Wing officials are insisting on nearly all of their demands for clamping down on the nation's immigration system, sources inside the White House and Capitol Hill said.

President Donald Trump had signaled to Senate Minority Leader Chuck Schumer that he was ready to take the deal on the table Friday afternoon -- a wall on the border in exchange for providing legal status for the undocumented immigrants known as the Dreamers, the sources said.

But sources with knowledge of the discussions said a wall alone does not come close to meeting White House demands.

"A wall does not equal border security," a senior administration official said, signaling the White House position on immigration is hardening.

An aide to a senior Democratic lawmaker laughed when told of that official's statement. Another key Democratic aide complained Schumer attempted to meet the President more than halfway, essentially offering to pay for Trump's signature campaign promise in exchange for protecting the Dreamers.

"We offered a massive amount (of money)," the Democratic aide said.

In the days leading up to the shutdown, Democratic lawmakers and strategists assumed Trump would take a "wall for Dreamers" deal, even pointing to Rep. Luis Guitierrez, D-Illinois, an immigration advocate, who has half-jokingly offered to help build Trump's wall.

"People like Luis think it's a fine agreement because the wall is not going to have that much of an impact," one strategist said. "Wall for Dreamers? Hell yeah. In a second."

Another calculation for immigration advocates is that the wall will never be built, even if the administration secures funding for the project. But the White House is well aware of those considerations, which is why senior officials close to the President are asking for more than just a wall.

In order to protect the Dreamers, a senior administration official said, Democrats will have to agree to the White House immigration wish list -- scrap the diversity lottery program, end so-called chain migration and give greater latitude to immigration officials to deport people who are apprehended.

That explains why hours White House chief of staff John Kelly turned down Schumer's offer.

"(Kelly) said it was too liberal," a Democratic aide close to the discussions said.

Inside the White House, the official said, there are serious doubts that Democrats will hold up their end of an immigration bargain.

"We're not trying to be greedy," a senior White House official said.

Administration officials have also adopted a tougher tone on the Dreamers, who were brought to the US as children by their parents. They are now frequently referred to as illegal or unlawful immigrants despite the fact that they entered the nation through no fault of their own.

"We will not negotiate on paying border patrol, the military and TSA in exchange for benefits for illegals," an official said of the group of undocumented immigrants.

An end to the shutdown that reopens the immigration debate will remind Democrats of their weakened position in Washington. One Democratic strategist predicted Schumer is likely to face criticism in the party's progressive base over his decision to offer to pay for Trump's wall.

"That's tricky territory," the strategist said.