WASHINGTON — The federal official in charge of health insurance shopping malls, which open Tuesday under President Obama’s health care law, has been challenging conventional wisdom since he came to Washington from California three and a half years ago.

The official, Gary M. Cohen, is at the center of the furor over the health care law. As director of the Center for Consumer Information and Insurance Oversight, he enforces the provisions of the Affordable Care Act that affect insurance companies. He supervises the new insurance marketplaces, or exchanges, including more than 30 that will be run by the federal government.

Mr. Cohen has been a punching bag for Republicans in Congress, who see him as the embodiment of a big-government approach to social policy. Even some Democrats have chided him, saying he needed to speed work on the exchanges so people could sign up this week, for coverage that begins as early as Jan. 1.

Through it all, Mr. Cohen, 58, has maintained a grim sense of humor.

On his Facebook page, he posted a link to one particularly grueling session — “the long-awaited video of my grilling” at a recent Congressional hearing — where a Republican lawmaker called his answers irresponsible, appalling and reprehensible.

A graduate of the Fieldston School in the Bronx, Brown University and Stanford Law School, Mr. Cohen was a litigator at Keker & Van Nest, a San Francisco law firm, for 16 years. He sharpened his skills as a regulator working at the California Public Utilities Commission and the state’s Department of Insurance, then headed by John Garamendi, a Democrat, who went on to become lieutenant governor and is now a member of the United States House of Representatives from Northern California.

“We worked together to build the toughest consumer protection agency in America,” Mr. Garamendi said in an interview. “There could not be a better person for the insurance exchanges.”

Harvey J. Rosenfield, the founder of Consumer Watchdog, an advocacy group based in California, said: “Gary has a fabulous combination of skills that you rarely find in one person. He’s very shrewd politically and very smart as a lawyer. In daily battles with the insurance industry, he intervened to make sure consumers were not only heard, but also protected.”

Mr. Cohen has repeatedly assured Congress that the insurance exchanges would be ready on Oct. 1. But his forecasts look a bit rosy in retrospect, as computer problems and technical glitches have forced the federal government and some states to delay features of the online markets. Mr. Cohen has sometimes sounded unfamiliar with operational details of the exchanges, which rely heavily on computer technology to display health plan options and premiums, calculate subsidies and enroll consumers.

Mr. Cohen describes his work as an adventure. On his personal blog, Mr. Cohen Goes to Washington, he said the 2010 health law signaled “a new day in health care in America,” promising coverage as a right, not a privilege.

Mr. Cohen and his wife, Elizabeth Nichols, started dating in high school. His father, Harold D. Cohen, was an agent and producer in the entertainment industry, and Mr. Cohen understands that Washington is often a stage for political theater.

His observations on the threat of a government shutdown in 2011 are pertinent today. “The madness that has been going on here shows no signs of letting up,” he wrote on his blog, which has not been updated since.

Mr. Cohen has held several high-profile health care jobs in recent years. He gained state experience when he served, for several months in 2012, as chief counsel of California’s insurance exchange.

In California and in Washington, Mr. Cohen has challenged the view that new ideas will fail in the future because they were tried and failed in the past.

“Those who remember the past are condemned to repeat it,” Mr. Cohen says, inverting the philosopher George Santayana’s famous aphorism.

“Institutional knowledge is coin of the realm around here, and since I have none, it is natural that I should be somewhat impatient with it,” he said.

In 2010, Mr. Cohen was the chief of staff in Mr. Garamendi’s Congressional office, and some of his most revealing blog posts date from that time.

Republicans, he wrote, “just don’t care about what’s good for the country.”

A year later, after visiting Civil War battlefields in Northern Virginia, Mr. Cohen said he could not understand the veneration for Robert E. Lee and other Confederate generals who defended a slave-owning society.

“Why,” he asked, “wasn’t Lee taken out and shot as a traitor?”

The federal government will run the exchanges in most Southern states, where officials have refused to. By most accounts, Mr. Cohen and his team are working well with those states.