WASHINGTON —  A provision to boost education for members of the military is drawing the ire of a budget-minded group of Democrats because House leaders have not found a way to pay for the program, a snag that holds the possibility of breaking apart the Iraq war funding bill.

The Blue Dog Coalition, a group of 47 moderate House Democrats, flagged the bill because the component known as the new G.I. Bill isn't paid for. The G.I. Bill portion alone would cost about $720 million the first year, but more as time passes on.

President Bush has asked for $100 billion to pay for the wars in Iraq and Afghanistan between now and the end of September. Democrats have crafted the bill so it provides about $96 billion of that request, plus $100 billion in other unrelated programs including health care and unemployment benefits.

Without support of the Blue Dogs, the bill could face a tough vote. Potentially more embarrassing would be a defeat of the "rule" which sets the terms of debate. A failure to pass the rule blocks the bill from coming to the House floor at all.

Rep. Allen Boyd, D-Fla., a Blue Dog co-chairman, says the legislation is an opportunity for the Blue Dogs to the gain the attention of Democratic leaders on the Hill. Blue Dogs held their noses last December when they eventually had to vote an unpaid fix of the Alternative Minimum Tax. At the time, Blue Dogs threatened to hold Congress in over Christmas until the AMT was paid for, but when they relented, the Blue Dogs said leadership heard their complaints.

At the start of this Congress, House Speaker Nancy Pelosi, D-Calif., said that all bills would be paid for: They would either be revenue-neutral or create a new revenue source to offset new costs.

FOX News' Chad Pergram and The Associated Press contributed to this report.