WASHINGTON – The Obama administration is launching a special coverage program for uninsured Americans with medical problems this week, the most ambitious early investment of President Obama’s health care overhaul.

But here’s the catch: Premiums will be a stretch for many, even after government subsidies to bring rates close to what healthier groups of people are charged.

And $5 billion that Congress allocated for it through 2013 could run out well before that.

The Pre-Existing Condition Insurance Plan will begin accepting applications in many states on Thursday, with coverage available as early as Aug. 1, an administration official said Tuesday. Consumers can check availability in their states on a new website, healthcare.gov, starting Thursday. The goal is for all states to be enrolling people by the end of the summer.

The official spoke on condition of anonymity ahead of the administration’s announcement later this week.

“I would enroll as soon as you can,” said Stephen Finan, policy director for the American Cancer Society Cancer Action Network. “These rates are going to be as affordable as consumers can get these days, particularly for a high-risk individual.”

Premiums will vary from state to state. In California, for example, the cost for a 50-year-old is estimated at $575 a month, with a $1,500 annual deductible and 15 percent co-insurance.