In addition to his remarks about the GOP "re-grouping," Sen. John CornynJohn CornynRand's reversal advances Pompeo Joe Scarborough predicts Trump won't run in 2020 Republicans divided over legislation protecting Mueller MORE also reignited the debate over immigration Thursday morning.

Speaking on MSNBC, Cornyn said he was "disappointed" with President Obama's remarks on immigration reform at Wednesday's press conference.

"I was a little disappointed to hear the president backtrack last night on his commitment to deal with this in the first hundred days of his presidency," Cornyn said. "This is an issue that has been around a long time."

"I'd like to see the president's plan," Cornyn went on. "That's part of leadership, and that's the only way this is going to get done with the president laying out for the members of Congress what his plan is and rallying people to try to deal with this very difficult and complex issue."

Obama said Wednesday that he is committed to forming a working group on immigration reform. He also said he is taking administrative steps, such as strengthening security on the border, to pave the way for larger reforms.

That didn't satisfy Cornyn.

"Well, forming a working group to think about what the process might be... it's backtracking on his commitment to deal with this."