WASHINGTON—Medical-device companies scored a political victory when the Senate voted in a non-binding resolution to repeal a new device tax, and now they are turning their attention to the House, especially U.S. Representative Ed Markey.

The 2.3 percent tax went into effect in January and is supposed to help offset the costs of implementing President Obama’s landmark health reform law. But the device industry argues that it would cost Massachusetts’ largest companies more than $411 million a year, according to a new analysis by the Pioneer Institute that will be released in April, just before the first payment is due.

The Senate voted 79-20 to repeal the tax Thursday evening in a bipartisan budget amendment in a non-binding resolution. Massachusetts Senators Elizabeth Warren and William “Mo” Cowan signed on to the repeal, following a flurry of last-minute lobbying from Massachusetts medical device makers of New England Democrats.

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A House version of the bill, sponsored by U.S. Representative Erik Paulsen, a Minnesota Republican, has drawn 212 cosponsors, including four Massachusetts Democrats: Niki Tsongas of Lowell, Michael Capuano of Somerville, William Keating of Bourne and Stephen Lynch of South Boston.

Lynch and Markey are vying in a Democratic primary contest for the Senate seat vacated by Secretary of State John Kerry. (Cowan is temporarily filling the seat.) Markey, the longest serving member of the delegation, voted against repealing the medical-device tax last year. Lynch voted against it as well.

Markey says he has not signed onto the current bill because it does not specify how the repeal would be paid for.

“I am concerned about the impact that the device tax could have on the medical device industry and job creation in Massachusetts,” Markey said. “I opposed the inclusion of this tax in the House health care reform bill. I would support repealing the tax, as long as the revenue replacing it does not impact middle-class families or their health care benefits.”

Kirsten Hughes, MassGOP chairman, urged Markey to support the current repeal effort. “This tax has already destroyed the jobs of Massachusetts families while thousands more hang in the balance,” Hughes said. “It is time Markey put the interests of Massachusetts above those of the far-left D.C. crowd.”

Warren, who campaigned against the tax last year in a tough race against Republican Scott Brown, a device industry ally, had set off concerns within the industry when she did not become an early sponsor of the bill by Senators Orrin Hatch, a Utah Republican, and Minnesota Democrat Amy Klobuchar to undo the tax. Warren had said she supported repealing the tax but wanted to make sure doing so would not take money away from the healthcare law.

The senate bill to repeal the tax calls for an offset to be identified later.

“While it is non-binding, we believe it serves as an important backdrop for future consideration of the full repeal of the medical device tax,” said Tom Sommer, president of Massachusetts Medical Device Industry Council. “Work now focuses on identifying the offset and carrying it forward.”

Massachusetts, the second largest medical device producer behind Califonia, employs about 24,000 people in the industry. A survey of Bay State companies by MassMEDIC found that in response to the tax, companies plan to reduce their research and development budgets, shrink the size of their workforce, and pass on the tax to hospitals and patients.