WASHINGTON — Americans for Prosperity, the political group backed by the billionaire brothers Charles and David Koch, is targeting three of the most vulnerable Senate Democrats who are up for re-election next year. The group’s efforts are part of a new $3.5 million attack advertising campaign that hammers lawmakers for supporting President Obama’s health care law.

The senators — Mark Begich of Alaska, Kay Hagan of North Carolina and Mary L. Landrieu of Louisiana — are all from conservative-leaning states that voted to elect Mitt Romney in 2012. The ads will start running in those states on Wednesday.

Americans for Prosperity is also targeting three Democratic members of the House who are in danger of losing next year: Ron Barber of Arizona, Joe Garcia of Florida and Patrick Murphy, also of Florida.

With the health care law’s flaws now front and center, Republicans and their allies have been trying to ratchet up the pressure on Democrats, especially where voters are most likely to respond negatively to the Affordable Care Act.

Tim Phillips, president of Americans for Prosperity, said that reminding voters about problems with the way the law had been carried out so far was part of a much larger strategy.

“We want to make sure Obamacare is the No. 1 issue they’re thinking about,” he said. “We believe repealing Obamacare is a long-term effort, and a key part of that effort is keeping it in front of the American people night and day.”

The ads are specifically aimed at women because the group’s research has shown that they are not only more undecided than men about the merits of the Affordable Care Act, but that they also tend to make the decisions about their family’s health care.

Women are featured as narrators in the ads.

“Health care isn’t about politics,” one of those narrators says in an ad that will be broadcast in North Carolina. “It’s not about a website that doesn’t work. It’s not about poll numbers or approval ratings. It’s about people. And millions of people have lost their health insurance.”

In the commercial that will run in Alaska, a woman talks about the unfulfilled promises made by Mr. Obama and senators like Mr. Begich: “Senator Begich didn’t listen. How can I ever trust him again? It just isn’t fair. Alaska deserves better.”