WASHINGTON — What if a new health plan set up shop in your town offering coverage at a much lower price than other insurers?

If you could save $2,500 on the $12,700 it costs for an average family plan through an employer, would you take it? That’s not small change.

Now what if the government offered that deal? Would your employer take it?

Americans may not yet have to choose if they’d be better off with government coverage, but lawmakers will be grappling with the consequences of such a decision when they return Monday after a weeklong July 4th break. Congress is facing a legislative sprint to meet a self-imposed deadline for separate House and Senate floor votes on a health care overhaul before lawmakers take their August recess.

President Barack Obama has said he wants to sign a bill in October that fulfills his goal of providing coverage to nearly 50 million Americans who lack coverage and reducing medical costs.

One of three main versions of the health care legislation — the bill crafted by House Democrats — includes provisions for a government-sponsored insurance plan that would be able to offer premiums 20 percent to 25 percent lower than private companies, according to an independent estimate.

Like no other issue, the debate over a publicly-administered plan has defined the differences between Democrats and Republicans over government’s role in health care. Democrats, who take credit for Medicare and Medicaid, say that a public plan would be good for the middle class as well. Republicans say it would lead to a government takeover of health care and put a damper on innovation in American medicine.

Strictly speaking, a public plan isn’t needed to cover the uninsured. The government could hand out vouchers to help people buy private coverage. But a government plan could help restrain health care costs that threaten to swamp the federal budget and are putting an ever greater strain on families and businesses alike.

“A public plan is able to basically not worry about profit or overhead,” said economist Karen Davis, president of the New York-based Commonwealth Fund. “They don’t advertise or pay commissions to brokers. The are able to pay providers rates that are adequate for the effective provision of care.”

Yet it could also fulfill the dire prophecy of the insurance industry that introducing government coverage would drive private companies out of business.

And that’s the dilemma for Obama, who supports a government plan.

A strong public plan that uses the government’s power to squeeze medical costs could bring about what Obama says he doesn’t want to do: disrupt what the president calls the “uniquely American” balance between government and employer coverage. Employers now provide coverage for more than 160 million Americans.

“You can’t have it both ways,” said Mark McClellan, who ran Medicare for President George W. Bush. “Either the government plan can get substantially lower costs by exerting power that other health plans don’t have. Or, if you go the other way, and you don’t give the public plan any special advantages, and you make sure it doesn’t get too big — in that case it’s not going to be any less costly.”

“So what’s the point?” McClellan adds.

Obama hasn’t said how he thinks the balance should be struck, so lawmakers in Congress are taking widely varying approaches.

In both the House and Senate versions, a public plan would be available through a new kind of insurance purchasing pool called an “exchange.” People buying coverage through the exchanges would have a choice of several private plans, as well as the public option.

The similarities would end there.

The Senate is looking at several options, including independent, nonprofit co-ops and a government plan that in key ways is designed to operate like private insurance. In the Senate legislation, it’s likely that only individuals and small businesses would be able to sign up in the public plan.

House Democrats have taken another path.

They’re proposing a government-run plan that initially would be open to individuals and small businesses, but could include all employers within three years. It would pay medical providers using rates similar to what Medicare pays, which is typically less than what private insurance pays.

The effects would be dramatic, according to an analysis of the House bill by the Lewin Group, a numbers crunching firm that serves health industry and government clients. A Medicare-like plan would be able to offer premiums as much as 25 percent lower than private coverage.

If the plan is eventually opened to all employers, it would sign up 123 million people. Meanwhile, the number of people with private coverage would plummet by about 114 million.

“If we create this public plan which is priced so much lower than private insurance, that will draw a lot of people in,” said John Sheils, a Lewin vice president. “Then you might wake up one morning and say, ’Wow! There’s only one payer.’ “