The veterans groups opposing the House legislation — including Disabled American Veterans, Iraq and Afghanistan Veterans of America, Veterans of Foreign Wars and Vietnam Veterans of America — wield considerable influence in Washington, and their opposition is taken seriously on Capitol Hill.

They sent a stern letter to lawmakers on Saturday objecting to the bill’s terms and spent the weekend lobbying congressional staff members. They say the plan, which provides $2 billion to cover Choice program expenses for six months without adding any funds to departmental programs, would push veterans out of the latter without addressing the systemic problems that prompted the creation of the program in the first place.

“You just can’t give money to send people out of the system while neglecting to put money into the system to fix the capacity problem that is there,” said Garry Augustine, the Washington director for Disabled American Veterans. “We believe that is a slippery slope to dismantling the V.A.”

To be sure, the opposition from veterans groups was not unanimous. Several large groups declined to stake out a position, and at least one, the Concerned Veterans for America, embraced the plan. This small conservative advocacy organization linked to the free-market activist billionaires Charles G. and David H. Koch has long made it its mission to offer more private sector choices for veterans’ health care.

During a debate preceding the vote on Monday afternoon, Representative Phil Roe, Republican of Tennessee and the chairman of the House Veterans Affairs Committee, said he valued the veterans groups’ feedback but disagreed that the short-term measure would push the department toward privatization. He also said he did not agree that departmental programs were lacking for funds. A spokesman for Mr. Roe, Tiffany Haverly, said he was committed to finding a solution to ensure veterans did not lose access to care through the program.

Mr. Roe and Republican leaders had been confident enough in the bill’s chances that they chose to pass it under an expedited process — usually reserved for uncontroversial measures like post office namings — that requires a two-thirds majority. It backfired after Democrats began to slip away in recent days.

The committee’s top Democrat, Representative Tim Walz of Minnesota, had implored House leaders to delay the vote to give both chambers time to strike a deal and took issue with how the $2 billion extension was funded. Rather than require that the extension funds be offset, he said, Congress should grant the funding on an emergency basis.