Sen. Lindsey Graham Lindsey Olin GrahamSenate GOP aims to confirm Trump court pick by Oct. 29: report The Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting Senate GOP sees early Supreme Court vote as political booster shot MORE (R-S.C.) rolled out legislation on Wednesday to overhaul the country’s asylum laws, including increasing the amount of time an undocumented minor can be detained.

Graham, speaking at a press conference, said the country’s current laws are “incentivizing a horrible journey … through hell."

“People are trying to get caught," he told reporters. "They will keep coming because they want to get caught."

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Graham’s legislation would overhaul the U.S. asylum system, including increasing the number of days a family can be held together from 20 to 100. Democrats are likely to balk at changes to the Flores settlement, which limits the amount of time a minor can be held in custody to 20 days.

“This is a nightmare for smugglers,” Graham said, referring to his legislation, adding that “what I’m trying to do is cut off the faucet.”

In addition to changing the Flores settlement, Graham’s legislation would require asylum claims to be filed in Mexico or a home country, instead of in the United States.

It would also provide funding for 500 new immigration judges and allow for unaccompanied minors from Central America to be set back to their home countries, similar to unaccompanied minors from Canada or Mexico.

Graham's legislation comes after White House adviser and son-in-law Jared Kushner Jared Corey KushnerAbraham Accords: New hope for peace in Middle East Tenants in Kushner building file lawsuit alleging dangerous living conditions Trump hosts Israel, UAE, Bahrain for historic signing MORE, policy adviser Stephen Miller Stephen MillerSpecial counsel investigating DeVos for potential Hatch Act violation: report Trump confirms another White House staffer tested positive for COVID-19 Biden pick creates furor, underscoring bitterness over Obama immigration policy MORE and Vice President Pence briefed GOP senators Tuesday on the White House's forthcoming plan to overhaul legal immigration.

Graham said that his legislation lines up with the asylum provisions in Trump's plan, but the White House proposal deals more broadly with legal immigration and shifting who gets green cards.

Graham urged for "Tuesday Trump" to show up to negotiate immigration legislation, referring to a White House meeting where the president gathered with a bipartisan group of lawmakers and told them to send him a bill and he would sign it.

"If we can find a reasonable solution … and the president says no to more immigration reforms, then I think he will own this problem," Graham said.

"Here's the task for you, Mr. President: You had a meeting with Republicans and Democrats. You said 'send me a bill and I will sign it.' We sent him a bill, and he didn't sign it. So I am urging the president to lead us to a solution," Graham added.

But any legislation faces an uphill, if not impossible, battle on Capitol Hill. Immigration has emerged as a fierce political issue during the Trump administration, with bases in both parties drawing a hard line on what sort of deal they would accept.

The Senate has nixed several immigration proposals during the Trump era. Two days after Trump urged lawmakers to bring him a plan, he also rejected a Senate proposal from a bipartisan group that included Graham.

Acting White House chief of staff Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE and acting Department of Homeland Security (DHS) Secretary Kevin McAleenan have met with Senate Democrats about potential changes on asylum, though Democrats, including Sen. Dick Durbin Richard (Dick) Joseph DurbinFeinstein 'surprised and taken aback' by suggestion she's not up for Supreme Court fight Grand jury charges no officers in Breonna Taylor death Democrats shoot down talk of expanding Supreme Court MORE (Ill.), have appeared skeptical about the chances of immigration legislation.

Graham called out both parties during his press conference, arguing that Congress has failed to address the U.S.-Mexico border.

"If you think this is a Trump-created problem, you really just hate Trump," Graham said. "And as a Republican, if you think we can just do this by building a wall, you're wrong."

He added that Democrats should ignore their "dislike and displeasure" with Trump and try to reach a deal.

Graham stressed that while his initial proposal was focused on asylum, he was willing to broaden it, including finding a solution on Deferred Action for Childhood Arrivals, in order to get 60 votes. Graham said he would hold a hearing and a markup of his legislation during the Senate's next work period, which runs through June.

"I'm willing to put other immigration ideas on the table to marry up with this," Graham said.