On the new Congress' first day, the House unanimously approved Republican legislation Tuesday making it easier for smaller companies to avoid providing health care coverage to their workers by hiring veterans.

The measure was approved 412-0 and is the first of many expected GOP bills aimed at President Barack Obama's health care overhaul, which was enacted over uniform Republican opposition.

That 2010 law is phasing in a requirement that companies with more than 50 full-time workers provide medical coverage for their workers. The House bill, sponsored by Rep. Rodney Davis, R-Ill., would exempt from that threshold veterans who already get health care from the Veterans Affairs Department or the military.

Supporters say the measure would encourage employers to hire veterans. That's a goal backed by members of both parties, even as federal figures show unemployment among Iraq and Afghanistan veterans dropped from 9.9 percent in November 2013 to 5.7 percent last November.

Critics say the measure's effect on companies and veterans is overstated. They say only modest numbers of firms are close to the 50-worker level and would be motivated to hire veterans to avoid providing medical insurance for their employees.

In a written statement, the White House said it backed the measure, saying it supports "commonsense improvements" in the law.

"We want to work with Congress on policies that strengthen and simplify the Affordable Care Act, protecting coverage and taxpayers alike," the White House said.

Rep. Paul Ryan, R-Wis., chairman of the House Ways and Means Committee, said he considered the bill "one piece of our ongoing efforts to fully repeal and replace" Obama's health care law.

Rep. Tulsi Gabbard, D-Hawaii, an Army National Guard member who has served in the Middle East, said the measure would help two important constituencies: veterans and small business.

"It's a great message and exactly the right tone" for the new Congress, Gabbard said.

A similar bill passed the House last year by 406-1, but went nowhere in the Democratic-run Senate. Sen. Roy Blunt, R-Mo., has introduced the same legislation in the Senate, which is now controlled by Republicans.

The House plans to debate a far more controversial bill later this week.

It would change the health care law's definition of a full-time worker from those who work 30 hours weekly to people working 40 hours.

Republicans say the health law's 30-hour requirement is encouraging companies to cut workers' hours.

Democrats say raising the law's threshold to 40 hours would put far more people at risk. That's because more employees work around 40 hours weekly than 30 hours, meaning that more of them could be targeted for fewer hours by companies looking to save money by reducing health coverage.