A veterans benefits bill that Republicans had hoped to pass ahead of the midterm elections is falling apart amid a battle over its cost. When House Republican leaders last week called off their final day of voting before the midterm elections and sent members home, they left behind a multibillion-dollar veterans benefits package they had once hoped would be a popular win to campaign on.

The sweeping bill, the Take Care of America’s Veterans Act, would devote critical resources to veterans benefits and programs. Instead, the legislation is stalled and on the brink of collapse, mired in a funding dispute that has divided the two parties, splintered Republicans and driven a bitter wedge between powerful veterans groups that normally band together when benefits are at stake.

The centerpiece of the bill is a provision that would allow service members who retired from the military because of a combat-related disability to receive their full retirement pay, rather than having it reduced dollar for dollar by their disability benefits, as current law requires. It is known as the Maj. Richard Star Act, named for a combat-injured Army veteran who advocated the policy change after he was forced to medically retire because of cancer that he developed from toxic exposure during deployments to the Middle East.

Republicans demanded that the cost of such a change — an estimated $9.4 billion over a decade — be covered by cuts elsewhere, and settled on paring back disability compensation for future veterans with sleep apnea and tinnitus. But Democrats resisted the trade-off and dropped their support for the entire package, which also would include funding for dozens of other veterans programs, from suicide prevention to lactation rooms at V.A. hospitals. So did some Republicans, who blasted an approach that they said pitted veterans against one another.