Pitched by the Democrats is a plan that would essentially guarantee a full-ride scholarship to any in-state public university, along with a monthly housing stipend, for individuals who serve the military for at least three years.
The proposal would give veterans 15 years to use the benefit, instead of the current 10-year limit, and would set up a new government program that matches financial aid by more expensive private institutions.
For a pricey public school - such as Miami University in Oxford, Ohio - that benefit might be worth as much as $31,000 per school year, compared to the maximum $9,900 benefit that veterans are given now.
The GI bill covered all the costs for World War II veterans. But today, with expenses exploding, the value of the benefit has plummeted, CBS News correspondent Thalia Assuras. Attending a public college costs an average of almost $13,000 a year. The GI bill pays about half that amount.
"Meeting the needs of our veterans is a cost of war," said House Speaker Nancy Pelosi, D-Calif., who described the bill as a "thank you" to the troops serving in Iraq and Afghanistan.
While Democratic leaders say they see a yes-vote on their proposal as a no-brainer for any lawmaker facing voters this fall, the new GI benefits plan has Republicans - and even some members of the more fiscally conservative Democratic rank-and-file - balking at the cost.
The nonpartisan Congressional Budget Office estimates that the proposal would cost $51.8 billion in the next 10 years.
The Pentagon has said that it's open to boosting college aid, even substantially, for veterans but wants the commitment to extend to at least six years, instead of three, before the full benefit kicks in.
"The last thing we want to do is create a situation in which we are losing our men and women who we have worked so hard to train," said Pentagon spokesman Geoff Morrell.
Republican Sens. John McCain of Arizona, Lindsey Graham of South Carolina and Richard Burr of North Carolina have proposed an alternative that would boost the maximum monthly stipend for GIs from $1,100 a month to $1,500 a month.
Democratic Sen. Jim Webb of Virginia counters that his legislation would be more effective in attracting new recruits and would offset any drop in the military's ranks.
"I can't think of a better way to broaden (the) propensity to serve than to offer a truly meaningful educational benefit, rather than simply taking that smaller demographic" of those already enlisted "and pound on it" with repeated combat tours, he said.
Democrats are pushing Webb's bill and other domestic add-ons, including a major expansion of state unemployment benefits, as part of a larger $195 billion package that would pay for the wars in Iraq and Afghanistan through early next year. A House vote is planned this week.
President Bush is expected to veto the measure if it is sent to him with added domestic spending, including the GI bill. In a closed-door meeting last week, Bush urged a group of House Republicans to reject the bill and uphold any veto if the legislation doesn't adhere to his request. Bush has indicated he supports a modest expansion of GI benefits - particularly allowing service members to transfer unused benefits to family members - but wants to address it in legislation separate from war spending.
Democrats are unlikely to heed his suggestion because it would lessen their leverage substantially.
Ultimately, Democratic lawmakers and their aides say they expect some version of the GI bill will pass eventually, even if they have to strip the domestic add-ons and find money elsewhere in the national budget to offset the costs.
But before they pare down their proposal, they plan to put Republicans on the spot - forcing them to either accept their domestic spending plan or go on record as opposing an effort widely endorsed by the nation's major veterans organizations.
"Visit Walter Reed," said Marty Conatser, head of the American Legion, in a recent statement urging Congress to pass the bill. "War is expensive indeed and the bulk of that cost is paid for by the men and women who wear the uniform. Benefits are just a small, small cost of war."
House Republicans acknowledge the upcoming vote will be a tough one. GOP members want to expand GI benefits, even if they think the Democratic proposal goes too far. And some Republicans whose home states have taken an economic hit also are likely to find it difficult to reject increased unemployment benefits.
Adding weight to the GI proposal are the military records of the bill's three leading co-sponsors in the Senate: Webb, a Vietnam war veteran and former Navy secretary; Republican Sen. John Warner of Virginia, former chairman of the Senate Armed Services Committee and a Navy enlistee during World War II; and Republican Sen. Chuck Hagel of Nebraska, a Vietnam veteran.
A companion bill in the House, introduced by Rep. Harry Mitchell, D-Ariz., has attracted more than 290 co-sponsors, or about two-thirds of that chamber.