WHEATON, Md. (AP) — Barack Obama on Tuesday sought acceptance of the new health overhaul law from skeptical seniors, a crucial constituency the White House wants to win over, even as the Gulf oil spill dominates public debate and the president’s time.

The questions Obama got from a large crowd at the Holiday Park Multipurpose Senior Center in suburban Maryland, and from others listening on the phone, suggested that even if rancorous debate has faded, plenty of doubts remain. And there’s only so much Obama can do to ease them. That may be a sobering prospect for the White House with crucial midterm elections looming.

Tuesday’s event was timed to coincide with the release later this week of the first batch of $250 checks to seniors who fall into Medicare’s prescription drug coverage gap, known as the “doughnut hole.” Some 4 million elderly and disabled people will get checks this year, a down payment on the law’s approach of closing the doughnut hole entirely over the next decade.

The first question Obama got, from a woman in the audience: Why can’t he close the doughnut hole faster?

Answer: “It’s very expensive.”

The next question was from a listener in Illinois who wanted to know whether participants in the private insurance plans in Medicare, called Medicare Advantage, would lose benefits.

The answer is yes, according to the Congressional Budget Office, but Obama didn’t come out and say it, explaining instead that Medicare Advantage plans are overpaid and subsidized by the majority of seniors who are on regular Medicare — something that’s also true.

Obama’s overall message: “What you need to know is the guaranteed Medicare benefits you’ve earned will not change … your guaranteed benefits will not change.”

He took shots at Republicans who want to repeal the law and said, “We’re going to fight any effort to go back to a system that doesn’t work for the American people and doesn’t work for our seniors.”

It might not be enough to reassure them.

Another question was from a laid-off worker in Nevada, too young for Medicare, who asked about losing COBRA subsidies that help him keep insurance.

Obama noted that the health law will help people like that join purchasing pools to gain competitive power to buy insurance. It won’t happen until 2014, so it won’t provide the immediate relief the Nevada worker is seeking.

But, Obama said optimistically, 2014 “is right around the corner.”

Copyright 2010 The Associated Press.