Veterans’ groups are storming Capitol Hill this week to press for an overhaul of the GI Bill to improve the education benefits provided to veterans of the wars in Iraq and Afghanistan.

The lobbying push has been gaining momentum in Congress in the past couple of weeks, with Senate Majority Leader Harry Reid (D-Nev.) lending his support for a bill introduced last year by Sens. Jim Webb (D-Va.) and Chuck Hagel (R-Neb.). That legislation mirrors the generous post-World War II GI Bill that helped veterans pay for their education and spurred a broad U.S. economic expansion.

“Momentum is finally building across America for a new GI Bill. This is something we can and must get done in Congress this year,” said Paul Rieckhoff, IAVA executive director, at a press conference.

“I hope that Senate leadership and my Republican colleagues take note of the overwhelming support for this initiative and will put partisanship and politics aside to address this national problem,” Webb said.

But despite bipartisan support in Congress — three Republican members have signed on as co-sponsors — the veterans’ groups may face an uphill battle in the White House and Pentagon. So far the administration has resisted the new GI Bill, fearing that the new benefits may prompt soldiers, sailors, Marines and airmen and -women to leave the military in favor of civilian life. Already struggling with re-enlistment, some Pentagon officials worry that expanded educational benefits could whittle down the force.

Webb’s bill also has yet to pass the Veterans’ Affairs Committee, to which it was referred last year. At a hearing Wednesday, the veterans’ groups pressed committee Chairman Daniel Akaka (D-Hawaii) to move the bill.

Meanwhile, Senate Armed Services Committee Chairman Carl Levin (D-Mich.) last week urged Defense Secretary Robert Gates to give Congress a formal Pentagon position on the bill within a month. Gates himself paid for his Ph.D. at Georgetown University with the help of the GI Bill.

“We are entitled to an answer,” Levin said last week.

At the same hearing, Sen. John Warner (R-Va.) said he wanted to “associate himself” with Webb’s “goals.” Warner’s support could give the bill a big boost, but by press time he had not been listed in The Congressional Record as a co-sponsor.

Rep. Robert “Bobby” Scott (D-Va.) introduced the House companion bill. It has attracted 93 co-sponsors.

Webb’s bill, which has 32 co-sponsors, would cover the full cost of attending a state university for in-state residents and provide a stipend for living expenses. The benefit is capped at the cost of the most expensive public state college or university. The total cost to the federal treasury is projected at about $2.5 billion per year.

Currently, the most a veteran can receive is approximately $9,600 a year for four years. Those who served combat tours with the National Guard or Reserves are eligible for even less — typically just $440 per month, or $5,280 a year.

By contrast, the College Board reports that the average four-year public college costs more than $65,000, about $16,250 a year, for an in-state student. A private university costs on average about $133,000 for four years.

The wars in Iraq and Afghanistan have relied heavily on the Reserve forces. Webb’s bill would ensure that reservists who served at least two years of active duty would receive the same benefit as the active-duty troops.

Currently, benefits used under the GI Bill count against federal student aid. And there is a 10-year limit on assistance for current educational benefits.

The original GI Bill provided full tuition, housing and living costs for some 8 million veterans.

In his most recent State of the Union speech, President Bush advocated for the ability to transfer current GI Bill benefits to spouses and children of veterans.

Sen. Kay Bailey Hutchison (R-Texas), together with Sen. Tim Johnson (D-S.D.) and a large number of co-sponsors, introduced a bill at the end of January to expand the eligibility of service members to transfer Montgomery GI Bill education benefits to immediate family members. The sponsors of the bill want to see it bypass normal committee procedure and receive a direct floor vote.