WASHINGTON — After weeks of failed immigration negotiations with members of Congress, President Donald Trump last week offered up his own loose outline of a deal on overhauling the country's immigration system and building a border wall.

But he's facing down skepticism from both sides of the aisle on Capitol Hill, where lawmakers have made little progress on a compromise in the week since Democratic concerns over the fate of roughly 800,000 immigrants brought to the country illegally as children touched off a brief shutdown of the federal government.

Louisiana's congressional delegation — seven Republicans and one Democrat — said little this week to suggest a bipartisan deal on immigration might be struck before Feb 8, the next deadline to extend funding for the federal government or face another shutdown.

Notes of hesitation from several of Louisiana's Republicans — as well sharp criticism from Rep. Cedric Richmond, D-New Orleans — illustrate the deep divide in Washington over an overhaul of the country's immigration system.

Several Louisiana Republicans in Washington sounded skeptical of the president's offer to include a potential path to citizenship for young people who are currently protected by an Obama-era program called Deferred Action for Childhood Arrivals, which Trump plans to cancel March 5 without congressional action. 

Some immigrants covered by the program have already lost protection when the federal government stopped renewing permits issued under the program. 

Top congressional Democrats had pitched a simple, narrow deal: codifying the DACA program into law in exchange for billions of dollars to build Trump's much-touted wall along the Mexican border.

But Louisiana's Republicans, and many of their colleagues in Congress, have appeared to rule that exchange out, instead drawing the fate of those immigrants into a much larger debate.

Among the potential items conservatives have put on the table: ending the legal diversity visa lottery, the family reunification immigration program, cracking down on so-called "sanctuary cities" and tightening up requirements for those seeking asylum in the United States.

"Anybody who thinks this debate is just going to be limited to amnesty for our DACA immigrants — they’ve been smoking some of that medicinal marijuana," said Sen. John Kennedy, R-La., just after voting to reopen the federal government Jan. 22. "Let’s go big. Moderation is for monks, as far as I’m concerned, and everything is on the table."

But Kennedy said it'd be "extremely unlikely" he'd back a bill that includes amnesty for immigrants who came into the country illegally or offers a pathway to citizenship for DACA recipients, commonly referred to as "Dreamers."

U.S. Rep. Garret Graves, R-Baton Rouge, said he's repeatedly asked constituents for their feelings on Trump's proposed outline — which includes a 10- to 12-year path to citizenship for the Dreamers along with $25 billion for a wall and deep cuts to legal immigration quotas — during remote town halls conducted on Facebook or by phone.

"People will just say, ‘no amnesty, no amnesty, no amnesty,'" Graves said.

"Certainly some of the president’s proposals give me pause," Graves added. "Is there a deal in there where you can do legal immigration reform and border security so much that we’d be willing to accept (something) while holding our nose? I don’t know."

Sen. Bill Cassidy, R-La., sounded more open Trump's proposed bargain. The deal has been repeatedly described as built around four elements: building a border wall, ending or cutting back on family reunification immigration — sometimes referred to as "chain migration" — scrapping the diversity visa lottery, which doles out 50,000 visas to applicants from countries with otherwise low rates of immigration to the U.S., and addressing DACA.

"Any one provision depends on the acceptance of the others because the net result of all four components strikes a balance," Cassidy said.

Reps. Ralph Abraham, R-Alto, and Clay Higgins, R-Port Barre, have signed onto a bill by Republican House Judiciary Committee Chairman Robert Goodlatte, of Virginia, that includes a pared-down version of the DACA program along with a number of restrictive immigration policies opposed by almost all Democrats.

The bill "ends chain migration, ends the visa lottery program, cracks down on sanctuary cities, mandates accountability for DACA illegal immigrants and authorizes greater border security including more boots on the ground and tactical wall infrastructure," Higgins said in a statement.

It's also seen as having no chance of passing the U.S. Senate, where Republicans hold a 51-49 majority but need at least 60 votes to pass legislation. A number of Senate Republicans have expressed concerns at the roughly 25 percent cut to legal immigration contained in the bill.

Graves said he anticipated that Republicans would end up gravitating toward something closer to what Goodlatte is proposing than the path to citizenship offered by Trump. But Graves also said deep cuts to the number of visas available to foreigners hoping to work in the U.S. also could push people to find unlawful ways into the country.

"If you make it too hard to come to the United States (legally), more people are going to come in illegally," Graves said.

Abraham sounded more hopeful. The Richland Parish physician said he was "more optimistic now than I ever have been" that a bipartisan deal on immigration could come together.

Abraham also didn't rule out backing a potential path to citizenship for Dreamers — though he said he'd "never" vote for broader amnesty — if it came along with tough border-security measures.

"Any deal that includes a pathway to citizenship for illegal immigrants must first include increased border security measures," Abraham said. "American citizenship is a privilege — not a right — and it has to be earned."

House Majority Whip Steve Scalise, a Jefferson Parish Republican who'll play a key role in pulling together enough votes to pass any deal party leaders might strike, called Trump's proposal "a starting point" toward addressing the country's "broken" immigration system.

"I look forward to working with (Trump) and my colleagues in Congress to build a consensus around a bill that secures our borders, provides funding to build a wall, ends chain migration, restores the rule of law and provides a clear path moving forward to stop illegal immigration from happening in the future," Scalise said in a statement.

But whether any such bill would have a chance of gaining enough Democratic support to clear the U.S. Senate remains an open question.

Richmond, the chairman of the Congressional Black Caucus, voiced the kinds of concerns Democrats have raised during the talks about immigration.

"Months ago, President Trump agreed to sign the Dream Act into law if it came with enhanced border security measures," Richmond said. "It is unacceptable that he has now moved the goal posts and demanded changes to legal immigration system."

Richmond also described the president's attacks on legal immigration programs as "cruel" and "a thinly veiled attempt to prevent immigrants of color from entering our country."

The opposition to Trump's outline points to the tricky political realities of immigration in Congress. A much-ballyhooed bipartisan Senate compromise in 2013 — brokered by the so-called Gang of Eight, including now-Minority Leader Chuck Schumer, of New York, and Florida Republican Marco Rubio — imploded amid opposition from House Republicans and left years of political fallout.

Kennedy said he'd like to see a wide-open debate on the Senate floor with every potential proposal up for discussion. But that doesn't mean Kennedy is optimistic about the Senate passing something.

"I’m not sure anything can get 60 votes," he said.

Follow Bryn Stole on Twitter, @BrynStole.