Cornyn told Republican colleagues at a meeting Wednesday that he would consider making changes to his amendment to bolster the border-security provisions of the Senate bill…

Cornyn said he’s willing to modify proposal but will not concede on what he calls its “fundamental substance.”

“There are certain elements that are non-negotiable, specifically the mechanism by which we would guarantee the security measures in the bill would actually be implemented,” he said.

The bill’s authors are also negotiating with Sens. Bob Corker (R-Tenn.) and John Hoeven (R-N.D.), but neither of those lawmakers have the same authority as Cornyn on border security.