Cornyn, a former Texas Supreme Court justice, said it’s inappropriate for states to interfere in the laws of other states.

“I do not understand the legal theory. I don’t want other states having a chance to change Texas law based on a similar effort. If you can do it for the election, you can do it if somebody wanted to challenge, for example, Texas law on the Second Amendment,” he said.

Senate Republican Whip John Thune (R-S.D.) said Thursday he agrees with Cornyn’s concerns.

“I just don’t know why a state like Texas which never wants anybody telling them what to do, now wants to tell a bunch of other states how to run their elections. I doubt the Supreme Court will take it up,” he said.

House Minority Leader Kevin McCarthy (Calif.), the top-ranking Republican in the lower chamber, declined to comment about the lawsuit when asked about it multiple times Thursday.