A panel of ten high-powered GOP pollsters said Republicans should look at Sen. Lindsey GrahamLindsey Olin GrahamOvernight Health Care — Presented by the Association of American Medical Colleges — Trump officials move to expand non-ObamaCare health plans | 'Zero tolerance' policy stirs fears in health community | New ObamaCare repeal plan McCain, Coons: Trump should withdraw controversial refugee nominee GOP senators drafting legislation to keep immigrant families together MORE's (R-S.C.) success more than House Majority Leader Eric CantorEric Ivan CantorThe Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Race for Republican Speaker rare chance to unify party for election Scalise allies upset over Ryan blindside on McCarthy endorsement MORE's (R-Va.) shocking defeat as they mull immigration reform.

The group, whose clients include much of the Republican conference in the House and Senate, came together to call for immigration reform and release poll results showing Republicans can win primaries while supporting the issue. The event was planned by FWD.us, a pro-reform group backed by Facebook founder Mark Zuckerberg.

Then Cantor lost the night before to professor Dave Brat (R), who attacked him on immigration reform. The results likely dealt a killing blow to any remaining chances of immigration reform moving anytime soon.

"I would caution against drawing any easy shorthand conclusions that immigration was the thing that drove the election," Republican pollster Jon Lerner argued. "On the same day that Eric Cantor lost Lindsey Graham won a pretty resounding victory in South Carolina."

"We had a great case study in how this issue plays out in a conservative Republican primary yesterday but it wasn't in the 7th district of Virginia, it was in South Carolina, one of the most conservative states," GOP pollster Whit Ayres argued, pointing out that Graham won big despite embracing comprehensive immigration reform while Cantor embraced only small parts of it."

Cantor's reelection campaign had some clear structural problems, when viewed in retrospect, and no one around him took Brat seriously until the race was called, partly because of inaccurate internal polling. Graham worked assiduously from the start to win his race. But the perception of Cantor's defeat clearly damages any hopes the group has of convincing skittish Republicans.

But while they didn't want to publicly admit it, those involved with the event privately acknowledged afterward that the biggest problem facing any movement on immigration reform was Republicans running scared — and on the perception that Cantor's loss was caused by his tepid support of reform.

One with many Capitol Hill clients said "there is no question" the perception among Republican members was that this was a dangerous issue to tackle and that Cantor's loss reinforced that with them.

"Their perception does not match the reality," another agreed.

Abby Smith contributed