The groups generally agree that McCain's approval is key to the bills' passage, The Washington Post said Thursday.
Measures that would increase veterans' education assistance and time off between assignments are expected to be voted on soon, the Post said.
A measure introduced Wednesday would provide more education aid to National Guard members and reservists, especially those who served multiple tours in Iraq.
"John McCain's got a lot of things to focus on right now, but this isn't one of them. He needs to get on board," said Vietnam veteran Sen. James Webb., D-Va., who wrote two of the veterans-related measures.
In an Internet ad, Iraq veteran Joshua Drake says, "If I could talk to John McCain, I would try to appeal to him as a fellow vet."
The group VoteVets.org delivered petitions containing nearly 30,000 signatures to McCain's Senate office, asking him to to back Webb's updated GI bill.
McCain's candidacy stresses his credentials as a veteran who understands U.S. defense policy. The Vietnam prisoner of war said he's "a consistent supporter of educational benefits for the men and women in the military."
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