WASHINGTON — One day after a televised meeting between nearly two dozen lawmakers and President Donald Trump, a group of bipartisan senators said they were increasingly optimistic about a deal on a handful of immigration issues that include border security and a solution on the future of thousands of undocumented immigrants currently caught in legal limbo.

Sen. Jeff Flake, R-Ariz., one of the six senators working on a deal, said Wednesday morning that they are “close” to an agreement. After an afternoon meeting with a group working on the deal, Flake emerged saying they “are closer.”

“We’re very close on the four categories that we outlined,” he said, adding that a deal could be announced as early as this week.

“I feel very positive we’re moving in the right direction,” Senator Dick Durbin, D-Ill., the lead Democrat in the talks, noted.

The proposal would address the nearly 800,000 undocumented immigrants who have been given protected immigration status under the Deferred Action for Childhood Arrivals — or DACA — program. Trump gave Congress until March 5 or the immigrants' protection would expire. The agreement is also expected to include additional border security, minor changes to family-based migration, and drastic changes to the diversity visa lottery program.

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The group, which also consists of Sens. Lindsey Graham, R-S.C.; Cory Gardner, R-Colo.; Michael Bennet, D-Colo.; and Bob Menendez, D-N.J., says their proposal should be able to obtain 60 votes in the Senate.

However, immigration legislation has been much harder to pass in the House over the last decade, and members there have had some complaints about the substance of the current negotiations in the Senate. “I understand that they’ve taken the kids hostage. There’s no other way to look at this,” Rep. Luis Gutierrez. D-Ill., said about the negotiations. “But tell me what the ransom is. Stop changing the terms of their freedom.”

The progress senators expressed hope for comes after a unique meeting with Trump on Tuesday, nearly an hour of which was televised. Even afterward, it remained unclear where the president stood on some of the key issues but members on both sides of the aisle said that the gathering helped move stalled talks forward by narrowing the parameters of any legislation.

Still unclear is what the president will accept when it comes to his much-touted border wall. After Tuesday's meeting, many legislators said that Trump signaled a willingness to back away from what some envision as a 2,000-mile continuous wall between the U.S. and Mexico.

“That helps for those who have envisioned this big concrete brick and mortar wall. It’s different. So that’s easier for the other side to accept,” Flake said.

But the president has not been clear on what he would accept and during a Wednesday news conference with Erna Solberg, the prime minister of Norway, he said any legislation must include the wall.

“It's got to include the wall. We need the wall for security; we need the wall for safety; we need the wall for stopping the drugs from pouring in,” Trump said.

Senate negotiators, however, are working off of Trump’s description of the wall in the meeting. A deal is expected to include authorization for about $1.6 billion of funding for about 700 miles worth of fencing for various spots along the border.

In addition to border security, other points of negotiation include the how to address the Dreamers, undocumented immigrants brought to the U.S. illegally as children. Durbin was adamant that any deal include a path to citizenship for all Dreamers, not just those who applied for the DACA program.

The six senators are also discussing family-based immigration, also referred to as chain migration. Negotiators wanted to keep discussions narrow and discussions revolve around prohibiting Dreamers from being able to provide their parents a path to citizenship but instead protected status.

And finally, they are discussing eliminating the diversity visa lottery, which allows 50,000 slots for people to apply to emigrate to the U.S., and giving those slots to immigrants already in the U.S. with protected status, including those from El Salvador and Haiti whose protected status was eliminated. The Congressional Black Caucus is expected to oppose any end to the diversity visa, however, because it would end most immigration from Africa.