WASHINGTON — Emboldened by the intense public criticism surrounding the rollout of the online insurance exchange, Republicans in Congress are refocusing their efforts from denying funds for the health care law to investigating it.

In changing tactics, Republicans hope to tamp down the continuing public criticism of their previously fruitless attack on the Affordable Care Act, one that led to a 16-day government shutdown, by focusing on the problems with the law that they say they have warned the nation about, unheeded, for three years.

“I think the biggest part of Congress’s job is to provide proper oversight of the executive branch of government,” Speaker John A. Boehner said Wednesday at a news conference. “And when it comes to Obamacare, clearly there is an awful lot that needs to be held accountable.”

Beginning Thursday, the House will hold the first of a series of hearings across multiple committees to examine the problems with the troubled Web site, as well as the law’s exemption and waiver components, and the problems that some consumers are having accessing their doctors through the program.