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The availability of employer-based coverage, the mainstay for working people and their families, remained stable this year, with 61 percent of all companies offering health benefits. However, only half of companies with 3 to 9 workers offered health insurance, while virtually all large firms with 1,000 or more employees did so.

Companies continued shifting costs to their workers, at a somewhat slower pace. A trend toward steering employees into plans with high annual deductibles eased a bit. The deductible is the amount you must pay each year before insurance kicks in. The survey found that 34 percent of workers are in plans with annual deductibles of at least $1,000 for single coverage, up from 31 percent in 2011.

“We don’t know if it’s a timeout, or if it’s reached some natural limit,” said Altman. “It’s really something to watch for in the future because (high deductible plans) have an impact both on people’s budgets and on holding down overall costs.”

The survey’s focus on health insurance provided to lower-wage workers highlights one of the major areas of uncertainty around Obama’s health care law.

If the president is reelected and the law goes into full effect, employers with lots of low-wage workers may be tempted to drop coverage and send their employees into new state-based insurance exchanges, markets that will offer taxpayer-subsidized private insurance. A separate survey this summer by the Mercer benefits consulting firm found that 9 percent of employers in the retail and hospitality industries say it’s likely they will drop coverage, even if they have to pay penalties to the government.

The survey found that workers in lower-wage companies pay $4,977 toward the cost of family coverage, as compared to an average of $4,316 for all workers. And the policy they get for their money is less generous, typically worth about $1,000 less.

“They are really paying more and getting less,” said Altman.

Although employers and government are doubling down on efforts to keep health care costs manageable, most experts believe the sluggish economy provides the likeliest explanation for the moderate rise in premiums. Last year’s spike is blamed on a mistaken bet by insurers that the economy would recover faster.

The survey includes more than 2,000 small and large employers. Asked what kind of increase they’re expecting for 2013, employers said their best estimate at this point is 7 percent — sure to prompt more pain.