(From CNN) – As part of his answer to whether he would reach out to Sen. John McCain as part of a renewed effort on immigration reform, the president said "we reach out to — to Senator McCain on a whole host of issues."

CNN asked McCain's spokeswoman if that's still true. She responded that the senator is actually going to the White House tomorrow with other Armed Services Commitee leaders to talk about procurement reform — a longtime issue for McCain.

However, McCain spokeswoman Brooke Buchanan also said that the White House mostly reaches out to the senator on issues where they have clear agreement, and she underscored a theme he brought up on the Senate floor just today — that he believes President Obama and Democrats don't really want to compromise on big, controversial issues.

"Reaching out and bringing ideas to the table with a real interest in compromise are two different things," Buchanan said.