Sen. James Lankford was one of the Republicans seeking a middle-ground deal on immigration last year, joining a series of bipartisan meetings where they tried to figure out how to legalize “Dreamers.”
But Mr. Lankford said every time he raised the other side of the issue — enforcement or limiting the chain of family migration — he was put off. Until finally he was just cut out of the meetings altogether.
“We literally stopped getting invited. I raised it every meeting for several meetings, and after that it was literally ’You’re no longer invited.’ Even when our staff contacted them and said when’s the next meeting — no response,” said the Oklahoma lawmaker.
Now, as Congress puts a government shutdown in the rearview mirror and begins to figure out how to return to the immigration issue, who’s actually in the negotiating room has become a major sticking point.
A number of different negotiating teams have emerged in recent months.
Mr. Lankford and Sen. Thom Tillis of North Carolina have written a bill dealing with Dreamers, while Sen. John Cornyn of Texas has introduced a border security proposal. Sens. Tom Cotton of Arkansas and David Perdue of Georgia have called for big changes to chain migration. All of them are Republicans.
Meanwhile Sens. Lindsey Graham, South Carolina Republican, and Richard Durbin, Illinois Democrat, have led the bipartisan Gang of Six working on a broader legalization.
In the House, Judiciary Committee Chairman Bob Goodlatte, Virginia Republican, has a major enforcement bill, while a bipartisan team of Rep. Will Hurd, Texas Republican, and Pete Aguilar, California Democrat, have written a bill coupling border policy tweaks with a legalization.
But Democrats have said some of those Republicans shouldn’t be allowed in any talks.
Sen. Charles E. Schumer, Democrats’ floor leader, said Mr. Cotton and Mr. Goodlatte, who are focused on enforcement, would poison the chances for a bill Democrats could join.
“There is no deal those two could forge that would earn the support of a majority in either the House or the Senate,” said Mr. Schumer, New York Democrat. “If Sen. Cotton and Rep. Goodlatte, who have opposed [the Deferred Action for Childhood Arrivals program] all along and basically been strongly anti-immigration have veto power over an agreement, everyone knows that there won’t be an agreement.”
The White House has said it wants to see all sides — legalization-backing Democrats and enforcement-minded Republicans — work something out.
Rep. Luis V. Gutierrez, Illinois Democrat, said he told White House Chief of Staff John F. Kelly last week that won’t work.
“He wants people who don’t agree on immigration — that is people on the right wing of the Republican Party — to come in and have a say anyway,” Mr. Gutierrez said. “I think that’s the wrong way.”
Democrats have said the basis for any deal should be the talks between Mr. Graham and Mr. Durbin. But they’re the ones who cut out Mr. Lankford, Mr. Cotton and others.
Mr. Cotton said trusting them to negotiate will lead to a one-sided bill most Republicans can’t support.
“When Lindsey Graham and Dick Durbin agree on immigration, [that’s] not a bipartisan agreement — they agree on the policy. Lindsey Graham and Dick Durbin are not adversaries negotiating — they are allies strategizing,” Mr. Cotton said.
He also chided Mr. Schumer for trying to exclude him.
“I don’t understand why Sen. Schumer is so scared of me. He’s been around here for 38 years — you’d think he’d have more self-confidence in his negotiating abilities,” Mr. Cotton said. “I’m not scared of him or any other Democrat — I’ll talk to them about any issue at any time on any topic.”
The White House is pushing an alternative group consisting of the four deputy leaders of each chamber caucus. They are Mr. Cornyn, the second-ranking Republican in the Senate; House Majority Leader Kevin McCarthy; Mr. Durbin, the second-ranking Democrat in the Senate; and Rep. Steny H. Hoyer, the House minority whip.
Those four lawmakers began meeting earlier this month, but their talks were undercut by Mr. Graham and Mr. Durbin trying to strike their own deal.
President Trump, for his part, appears to be trying to empower senators to work on deals.
On Monday, as the immigration-infused shutdown was winding down, the president met with six Senate Republicans, including Mr. Lankford and Mr. Cornyn. He then held a separate meeting with Sens. Joe Manchin of West Virginia and Doug Jones of Alabama, two more conservative Democrats.
The senators emerged to say they had good talks, but didn’t get into policy — though they agreed border security must be part of any final package.
“His intention is to do bipartisan deals,” Mr. Manchin said.
• S.A. Miller contributed to this article.
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