“We oppose mass roundups and mass deportations, we think it’s too costly and unnecessary [and] anything that pulls back from that we’re glad to see,” Roy Beck, head of at NumbersUSA, which advocates for a reduction in immigration, said Tuesday by phone. “It seems like that is the direction that Mr. Trump is going in right now. And if that’s the case then we applaud it.”

Rep. Steve King (R-Iowa), the House’s immigration hardliner, echoed that message. King warned that while a shift in positions “would be a mistake,” a moderation in tone is “fine.”

“I would expect that softening this tone is something that may be part of this new campaign,” King told CNN Wednesday.

Sen. Jeff Sessions (R-Ala.), an early Trump supporter who’s the face of hard-line immigration policy on Capitol Hill, said after Saturday’s Hispanic outreach meeting that Trump is “wrestling” with how to approach the 11 million people living in the country illegally, but he’s in no way backtracked from earlier vows to hold them accountable.

“First and foremost he has made clear that we end the illegality,” Sessions told CBS’s “Face the Nation” on Sunday.