Senator McCain has already released a television ad responding to Senator Barack Obama's VP pick.
The ad, entitled "Biden," highlights the fact that Senator Joe Biden questioned Barack Obama's lack of experience and said he would be, quote, "honored" to run with John McCain before he was selected to run on the Democratic ticket.
McCain's campaign said the ad shows Biden is Obama's "harshest critic."
The ad is expected to air in key states.
Meanwhile Republican John McCain hinted Saturday that his own choice for a running mate will be unveiled soon.
McCain seems to have eliminated the possibility of choosing a pro-choice vice presidential candidate, like Tom Ridge or Joe Lieberman.
Analysts say that leaves his former rival Mitt Romney, and Minnesota Governor Tim Pawlenty on his short list.