"It would be a national, not-for-profit," Brown said. "(The Office of Personnel Management) would administer it. It would be any number of national not-for-profits that would compete nationally and they would take the place - more conservative members hope - of the public option. They would be in states and be running a kind of lookalike to a public option.

Existing insurance companies could participate as long as their plan is not-for-profit, he said.

Somehow I can't envision a Blue Cross/Blue Shield not-for-profit doing anything that would put downward pressure on their for profit insurance plans.

The reason why Senators, Congressmen and their staffs are so happy with their health plans is that they themselves are or are connected to politically powerful individuals.  The rest of the federal government employee unverse fares only slightly better through the labyrinth than the average American, and that's because they have protections as federal employees.  Protections that I don't imagine would extend to the greater universe of participants not directly employed by the federal goverment.

This set up even in its current limited model for federal employees is a subsidy for the private insurers.  There really is no reason why federal employees shouldn't be covered by a government program too.  No reason other than to subsidize the private insurance companies that is.

From the pdf:

What is FEHBP?

• FEHBP is a private insurance program that the federal government offers to its employees, including the President and members of Congress.

• An example of "managed competition," FEHBP is a system of over 100 competing private health plans offered by private insurance companies or employee associations such as labor unions. The majority of enrollment, however, is concentrated in just a few plans.

• Like almost all private insurance plans today, the plans offered under FEHBP stipulate (i)which physicians you can see, (ii) which drugs your physician can prescribe, (iii) whether you can see a specialist, and (iv) whether and where you can be hospitalized. You can be turned down for treatment.

• Like almost all private insurance plans today, the plans offered under FEHBP stipulate (i) which physicians you can see, (ii) which drugs your physician can prescribe, (iii) whether you can see a specialist, and (iv) whether and where you can be hospitalized.  You can be turned down for treatment.

• Although FEHBP contracts only with health benefit carriers that offer a complete line of medical services, such as doctor's office visits, hospitalization, emergency care, prescription drug coverage, and treatment of mental conditions and substance abuse, there is no standard prescribed minimum benefit package and benefits vary from plan to plan.

• The government pays a significant portion of each employee's insurance premium, covering either 72 percent of the average FEHBP plan premium, weighted by enrollment, or 75 percent of the premium for the plan chosen, whichever is less.  The enrollee pays the difference.  This is a better deal than many non-government employees get; in 2008, nearly half of employer-insured individuals paid more than 25 percent of the total premium for family coverage.

What your tax money will also subsidize:

ThinkProgess has documented how the private health insurance industry is waging a duplicitous, "two-faced" campaign to kill health reform. Because the industry understands that the public views it in a largely negative light, the industry presents itself as proactively working hand-in-hand with legislators to produce reform. However, behind the scenes, the industry is coordinating a massive effort to kill all reform -- employing attacks from front groups, allied politicians, think tanks, lobbyists, and right-wing media.
...
Yesterday, the BCBS Association released yet another industry-sponsored study to distort health reform and falsely claim that premiums will skyrocket because of the legislation. However, the nonpartisan CBO reported earlier this week that under the Senate health reform bill, "most Americans would pay the same or less in premiums." A New York Times editorial yesterday criticized BCBS Association's study, and noted correctly that it is yet another example of the private insurance industry doing whatever it can to frighten Americans. link

Existing insurance companies could just participate and say "sure, it's not for profit". But how do you verify that? What would be the conditions?