[Redbob]

Of the lasts 3 major figures Texas has sent to Washington, 2 have been major embarrassments*;
the third is John Cornyn, famous for his staunch opposition on the Immigration Bill Committee to John McLame’s efforts to insitutionalize Amnesty!
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* I’m referring of course to Bush the Younger, and K.Bailey Hutchison, R-Uranus.

[Texas Federalist]

the third is John Cornyn, famous for his staunch opposition on the Immigration Bill Committee to John McLame’s efforts to insitutionalize Amnesty!

He initially supported the bill. He just decided to listen to the outcry sooner than everyone else. I'll give him credit for listening to conservatives more than the other two. However, he certainly isn't a conservative "leader" like Sessions, DeMint or Coburn.