WASHINGTON — A health program for veterans that President Trump heralds as a triumphant success is struggling to make its network of doctors as large as required to meet an aggressive expansion of care outside the Department of Veterans Affairs health facilities, officials said. The company managing the new program in a majority of the states said it would probably need millions of dollars more to meet the plan’s coverage goals.

Under a new law, known as the Mission Act , veterans who need to drive for at least 30 minutes to a government-operated veterans hospital — rather than 40 miles under old standards — can receive primary care and mental health services outside the department’s traditional system. The switch for the nine million enrollees in the program for veterans was the biggest shift in American health care since the passage of the Affordable Care Act under President Barack Obama, potentially moving tens of thousands from government services to private care.

Officials at Optum Public Sector Solutions, the third-party administrator for the new health plan for veterans across a large portion of the United States, recently told congressional aides that they were unable to guarantee a health care network large enough to accommodate all the veterans who might seek care under the new system. They suggested that more money — perhaps as much as $75 million — would be needed to help build a larger network. The contracts for their region, complete with seven renewable one-year options through 2026, were worth a potential total of $55.2 billion. Their region includes 36 states in the eastern half of the United States, as well as the District of Columbia, Puerto Rico and the Virgin Islands.

“The $75 million figure is an early estimate based on nothing more than guesswork,” said Christina Mandreucci , a spokeswoman for the veterans department. “While there are almost always costs involved in contract modification, both V.A. and Optum believe they will be a fraction of that total, with future estimates driven by network utilization data.”