John McCainJohn McCainTrudeau, Trump speak for second night about US-Canada trade McCain: China has done ‘nothing’ on North Korea Trump administration weighing order to withdraw from NAFTA MORE, who refused to support a bipartisan measure expanding the G.I. Bill proposed by Sen. Jim Webb (D-Va.), put forth his own proposal Tuesday.

McCain, Sen. Lindsey GrahamLindsey GrahamComey to testify before Senate Judiciary Committee Overnight Defense: US moving missile defense system to South Korea | Dems want justification for Syria strike | Army pick pushes back against critics of LGBT record Graham: There are 'no good choices left' with North Korea MORE (R-S.C.) and Sen. Richard BurrRichard BurrBurr: US in new Cold War with Russia Senator: No signs of GOP 'slow-walking' Russia investigation GOP senator hits back at criticism of Russia probe MORE (R-N.C.) are calling for an expansion of the Montgomery G.I. Bill, which has provided education benefits for members of the military. They aim to increase the $1,100 of education benefits per month for active duty service member to $1,500. That would increase to $2,000 per month for a member who served on active duty 12 years or more.

Webb's bill, which has the support of Democrats and Republican Sens. John Warner (Va.) and Chuck HagelChuck HagelLobbying World The US just attacked Syria. So where's Congress? Senators tear into Marines on nude photo scandal MORE (Neb.), also seeks to increase educational benefits for those in the military.

McCain had questioned whether Webb's bill provided enough incentive for its beneficiaries to stay in the military.

"We should encourage service members to remain in the military, and they should be rewarded with additional benefits if they do," he said in a release announcing his proposal.

McCain also had concerns over how the new benefits Webb called for would be administered and whether they could be transferred to family members, said McCain spokesman Robert Fischer.

The Veterans Affairs and Defense departments "know how to work with the current setup for G.I. benefits," Fischer said. "Our bill continues that administration, where Webb's bill creates a new administration delivery." Fischer added that McCain, Graham and Burr's bill would allow the G.I. Bill recipients to give half of their benefits to dependents after six years of service and the entire benefit after 12 years.

Webb spokeswoman Kimberly Hunter said that McCain's bill is more focused on career officers, not the entire volunteer military force. She said that Webb's benefit was designed for those in the military looking to transition to other careers.

"This military does a fine job of managing its career force, but when comes to... the 70 to 75 percent of service members who volunteered and did their time and decided not to re-enlist, they're being left behind and Sen. McCain's legislation continues to do this," Hunter said.

She added that Webb is working with Senate Veterans' Affairs Committee Chairman Daniel Akaka (D-Hawaii) to find a way to administer an enhanced G.I. Bill.

Read more about McCain, Graham and Burr's proposal here. Download a fact sheet of Webb's plan here (.pdf).