WASHINGTON — It was another turbulent week for President Obama’s health care law. Congress rejected a White House request for nearly $1 billion to carry out the law, even as federal responsibilities increased to include the supervision of insurance markets in more than half the states. Then, on Friday, Republican attacks on the law continued in the Senate, where Democrats beat back Republican proposals to repeal the law and many of its tax increases.

Federal officials are racing to set up insurance marketplaces, or exchanges, in 33 states — more than they ever expected.

Enrollment begins in six months, and the amount of work to be done is staggering, officials say.

Mr. Obama scored his biggest legislative achievement exactly three years ago when he signed the Affordable Care Act. But this week the administration cautioned officials to be careful about suggesting that the law would drive down costs.

After extensive research, the administration said it was unwise to tell consumers that they could get “health insurance that fits your budget.” That message, it said, is “seen as highly motivational, but not as believable.”