That aggressive campaign, which produced numerous hearings on the attacks in Benghazi, Libya, as well as on I.R.S. scrutiny of conservative groups, is now increasingly consumed by the health care fight. House Republican leaders empowered four committees — oversight, Ways and Means, Energy and Commerce, and Education and the Workforce — to take the lead, with support from other panels, such as the Science and Homeland Security Committees, which have examined computer security.

Mr. Cantor and Representative Cathy McMorris Rodgers of Washington, another member of the Republican leadership, have also leaned on all 231 House Republicans. A 17-page “House Republican Playbook” walks members through “messaging tools” like talking points, social media tactics and “digital fliers”; details lines of attack; offers up a sample opinion article for local newspapers; and provides an extensive timeline on the health care law and an exhaustive list of legislative responses that have gone nowhere.

A message of the week is presented to the Republican members at the beginning of each week, Ms. McMorris Rodgers said. A “Call to Action” email chain distributes relevant breaking news. A new website, gop.gov/yourstory, is collecting anecdotes from each member.

The goal, according to Ms. McMorris Rodgers, is to use all the “Republican voices we have in the House, the media markets in all the districts we represent, to take our message all over the country.”

“It penetrates,” she said. “It’s powerful.”

To Democrats, especially in the White House, the power of the effort stems from using anecdotes to paint a fundamentally misleading picture.

“There’s been so much noise and so much misinformation, and this incredible organized effort to block the notion that everybody should have affordable health care in this country,” President Obama told supporters of the health care law this month, “that I think it’s important for us to step back and take a look at what’s already been accomplished, because a lot of times it doesn’t make news. Controversies make news.”

Republicans have gone to the floor of the House and the Senate to tell constituent stories of soaring premiums or yawning new deductibles. But on Wednesday, the White House Council of Economic Advisers released a report showing that health care spending had grown by 1.3 percent since 2010, the year the health care law passed. That is the lowest rate on record for any three-year period and less than a third of the average since 1965, according to the White House.