Presidential spokesman Robert Gibbs said the idea was on the table as the administration sought "to maximize the resources available for veterans."
Veterans groups complained that the proposal would reverse government policy of taking responsibility for caring for the war wounded and said it could cause difficulties for veterans in getting future insurance or even jobs.
Members of Congress leapt in to join the criticism.
Leaders of about a dozen veterans groups met at the White House on Monday to discuss it with Obama and top administration officials. They returned for more talks with White House chief of staff Rahm Emanuel.
Gibbs' announcement that the idea was officially out was released by the White House in the afternoon.
"The president listened to concerns raised by the VSOs (veteran service organizations) that this might, under certain circumstances, affect veterans and their families' ability to access health care," Gibbs said. "Therefore, the president has instructed that its consideration be dropped."
Gibbs has noted that the administration is seeking an 11 percent increase in discretionary funds for the VA for this year. The proposal would have saved the Veterans Affairs Department hundreds of millions of dollars a year
The VA already pursues third-party billing for conditions that are not service-related. The process only applies to those veterans who have private health insurance.