One major disagreement has been in support of a new GI Bill, sponsored by Sen. Jim Webb, D-Va., which would expand benefits for those who serve. It passed the Senate with bipartisan support by a vote of 75-22 - a vote McCain missed while out campaigning.
The Arizona Senator, however, has said he objects to the bill, which President Bush has also threatened to veto.
Sen. Dick Durbin, D-Ill., said he hoped McCain would join Obama in supporting the bill, and suggested he meet with soldiers returning from Iraq and Afghanistan. "I think Senator McCain would come to realize that these veterans deserve the same good treatment coming back from this war as those who returned from World War II," Durbin said to Face The Nation host Bob Schieffer.
However, Sen. Lindsey Graham, R-S.C., characterized the new GI Bill as one that would "give $52 billion to the people who will leave the military and nothing for those who will stay."
Graham, in turn, suggested that because of changes on the ground in Iraq since Obama's last visit to that country in 2006, the Illinois Senator would benefit from another visit to the country to meet with officials there.
"Senator Obama keeps talking about an immediate withdrawal as soon as he gets to be president," Graham said. "I would recommend that he go back. So much has happened since 2006 on the ground. It's been extraordinary. He's never really had a one-on-one with General Petraeus. Go back and go to Iraq and talk to General Petraeus. Talk to the Maliki government and see how things have changed.
"I think if he would look at what's happened in Iraq, talk to General Petraeus and Maliki, I think he would have a different view of what you need to do next." He even recommended that McCain join Obama on the trip, so they could share in the briefings and fact-finding.
Durbin took exception with Graham's remarks, however, likening them to an ad created by a 527 committee, Veterans for Freedom (on whose advisory board Graham and Sen. Joe Lieberman, I-Conn., both sit). That ad accuses Obama of refusing to meet with General David Petraeus or go to Iraq.
"I would say to Senator Graham and Senator Lieberman, take a look at this ad," Durbin said. "This really is misleading and it really shouldn't be out in this part of the campaign. And I wonder how their being involved in it ... is consistent with Senator McCain's recent statement saying that if you have a title or a position in his campaign, you shouldn't get involved in a 527 that produces negative ads."
"I haven't been involved in anybody's ad," said Graham, who repeated that Obama has never sat down one-on-one with Petraeus.
Also on the program, Howard Wolfson, director of communications for Hillary Clinton's campaign, said that Clinton's remarks on Friday, bringing up the 1968 assassination of Robert F. Kennedy as an example of how nominating processes can extend late into the year, were blown out of proportion.
"To claim that she was making any kind of other reference in her comments is wrong and a misreading of what she said," Wolfson told Schieffer. "I think some in the news media did overhype this. I think that's unfortunate. ... So let's get to the facts of what she was saying, rather than what some in the media have interpreted she was saying."
Read the full "Face the Nation" transcript here.