NEW YORK (CNNMoney.com) -- The debate over whether to have a government-backed insurance plan is fast becoming the most divisive health care reform issue.

And it's a debate devoid of serious details about how such a plan would work. Those details, of course, will matter to supporters and opponents ... a lot.

"There are many ways to skin a cat," said Senate Finance Committee Chairman Max Baucus, D-Mont., a leader on the issue.

Of course, lawmakers are not entertaining an endless number of ways to craft a public plan. One option not on the table is a single-payer system -- whereby everyone would be enrolled in a national health insurance plan based on Medicare. Such a plan doesn't have the votes, according to Baucus and House Ways and Means Chairman Charles Rangel, D-N.Y.

But excluding the single-payer idea is where clarity in the debate ends. What form a public plan would take is anyone's guess.

A competitor to private insurers: Supporters of a public plan say it would push private insurers to lower costs and provide better coverage.

Private insurers fear a public plan will be too hard to compete with, especially if the government dictates how much it reimburses providers.

The House Progressive Caucus, which has more than 70 members, put out a statement on Monday calling for "robust" public option in the absence of a single-payer system, which many of its members would prefer.

Specifically, the caucus wants a plan that charges premiums "at the lowest levels possible, not tied to the rates of private insurance plans" and would "have the ability to structure the provider rates to promote quality care ... ." The caucus also wants a public plan to "establish or negotiate rates" with drug and health equipment companies "to achieve the lowest prices for consumers."

It opposes any provisions that would undermine or limit where or to whom the public plan is available.

Democrats on the Senate's Health, Education, Labor and Pension Committee want a public plan, said Sen. Chris Dodd, D-Conn., who is leading the charge in the absence of committee chairman Ted Kennedy due to brain cancer.

But a framework for one will be left out of its bill intentionally, Dodd said Tuesday. "I left those areas open for discussion -- not because they are open for some decision about whether or not we ought to move in that direction."

Other lawmakers worry an unbridled public option would set the stage for unfair competition.

Last week, after a meeting of key senators from both parties, Baucus said they had agreed on some basic principles if there is a public option, according to Congress Daily. "Make sure it doesn't set prices, [and] there really is competition, where government is very, very light."

A fallback: Fiscally conservative Democrats, known as the Blue Dogs, are not endorsing a public plan but will support one if it meets certain requirements.

Specifically, claims covered by a public plan would have to be paid for by premiums and co-payments. And reimbursement rates would have to be negotiated with the health care providers rather than based on Medicare rates.

The Blue Dogs, a 51-member coalition, don't want medical providers to be forced to participate. And the public plan must only be a "fallback" option triggered "in the absence of adequate competition and cost containment."

"We cannot create a public option that stacks the deck -- through rate setting and forced participation -- against a system that currently provides coverage to 160 million Americans," said Rep. Mike Ross, D-Ark., in a statement from the coalition.

One way a fallback could be structured is for a public plan to take effect immediately in areas where there's very little choice among insurance carriers. But it would only be triggered nationally if lawmakers determine cost containment hasn't worked.

"It's basically a threat [to private insurers]," said Paul Fronstin, director of the health research program at the Employee Benefit Research Institute.

A nonprofit cooperative: Sen. Kent Conrad, D-N.D., has suggested a possible compromise on a public plan option that could satisfy opponents who fear government control.

Conrad is floating a proposal that would create state-based or regionally based nonprofit co-op insurance plans in which participants pay into the plan and if there's any money left at the end of the year, it would be paid back to participants or used to lower premiums or improve benefits.

The co-op plans would be subject to the same rules as private insurers. And they would not be run by the federal government, although they might receive seed money from Uncle Sam. So whether a co-op plan would be considered "public" is a question mark.

And that could be its selling point.

On Monday, Baucus said, "we're trying to figure out a way to help keep the insurance companies' feet to the fire in a way that doesn't frighten Republicans away because it sounds too much like government."

How many people would join a public plan?

No matter the details of a public plan, there's no telling how it will alter the health insurance landscape.

"It's very difficult to say what people will do without looking at health reform in general," Fronstin said.

That's because the interaction between all the reforms eventually enacted could influence employers' decisions to keep or drop the coverage they offer.

For instance, some proposals mandate that individuals get insurance and that companies help them. There are proposals to set up a public insurance exchange in which consumers chooses from a bevy of health plans. And many proposals would prohibit insurers from denying anyone coverage based on health status.

Leaders from both parties say that however health reform is done, if you like the insurance plan you have, you can keep it.

"But what they don't say is [that it] may not be around any longer," Fronstin said.

- CNN congressional producer Ted Barrett contributed to this report.