House lawmakers opened the new legislative session by passing a measure billed as both a boost to veterans employment and a chance to roll back part of the president's controversial health care law.

The Hire More Heroes Act passed unanimously out of the chamber just hours after new House members were sworn into office. Republican leaders touted the effort as the start of their 2015 job-creation efforts.

"By making this commonsense change, we will not only provide small businesses with much-needed relief, but also help more of our veterans find work," bill sponsor Rep. Rodney Davis, R-Ill., said in his floor speech.

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The measure would allow businesses to hire veterans without having them count as full-time employees under the Affordable Care Act, provided the veterans already have health insurance through the Veterans Affairs or Defense departments.

Under the health care law, companies with 50 or more full-time workers must offer health insurance for their employees. Conservatives have maintained the rule discourages small companies from hiring new workers and growing into bigger, more successful firms.

House Democrats pushed back on that narrative and questioned whether Republicans were more interested in helping veterans or scoring a victory against the president's health care priorities. But that did not stop their support of the measure.

"Let's not undermine what is the purpose of this legislation," said Rep. Sander Levin, D-Mich. "Those who have served deserve as our priority any reasonable effort to provide them with the opportunity that they want. They have served. Now they want to work. We need to make sure they have that opportunity to work."

Last year, the House offered similar overwhelming support for an earlier version of the bill, but the measure stalled in the Senate. Leaders in the new Republican-run Senate have not said when they might consider the measure.

White House officials spent much of last week criticizing Republican efforts to roll back the Affordable Care Act, but also described the veterans jobs bill a "commonsense improvement to the law" that the administration will support.

The Congressional Budget Office has estimated the new law will cost nearly $860 million over the next decade, as some businesses will be able to avoid penalty payments for not providing private health insurance options.

Veterans unemployment has fallen steadily since 2011, according to Bureau of Labor Statistics data, and remained below national unemployment rates. But younger veterans have still struggled to find work, with jobless rates bouncing between 5 percent and 9 percent in 2014.

Davis said he's hopeful the measure will give recent war veterans with specialized skills "a leg up in a very competitive job market."