WASHINGTON — Democrats are increasingly anxious about an onslaught of television ads hitting vulnerable Senate and House candidates for their support of the new health law, since many lack the resources to fight back in the early stages of the midterm campaign.

Since September, Americans for Prosperity, a group financed in part by the billionaire Koch brothers, has spent an estimated $20 million on television advertising that calls out House and Senate Democrats by name for their support of the Affordable Care Act.

The unusually aggressive early run of television ads, which has been supplemented by other conservative initiatives, has gone largely unanswered, and strategists in both parties agree it is taking a toll on its targets.

Building on the success, the deep-pocketed organization disclosed on Tuesday that it was expanding its Senate efforts with $1.8 million in airtime to attack Democratic House members running for the Senate in Iowa and Michigan, where Democrats are viewed as holding an early advantage. The group was also moving into Montana, a state where Democrats may struggle to defend a seat, on behalf of a Republican House member running for the Senate.