Yes they do. It has been litigated more than once in the court under 1st amendment precedents.
First Amendment I don't think applies when the subject is about "CIA Leaks". Tim's 1st Amendment right is not being infringed.
And they loose the litigation. There is no protected speach between a reporter and a source. No matter what the press tells you. The Supreme Court has recognized the arguments made by the press as to its watchdog role in society, but it has not gone so far as to grant a reporter-source privilege.