If the traditional program cost more than the private plans, elderly beneficiaries would have to pay higher premiums.
Government data show that 5 percent of elderly beneficiaries account for more than 50 percent of all Medicare spending on the elderly.
Many elderly Americans have been outraged over a surtax levied on about 40 percent of the elderly beneficiaries to pay for the program.
The President was particularly careful to say that he would oppose new cuts in Medicare, whose elderly beneficiaries form a powerful political bloc.
Members of both parties had urged the administration to avoid any hint of penalizing elderly beneficiaries who stay in traditional Medicare.
The association said that elderly beneficiaries spent an average of $2,149, or 19 percent of their income, on health care last year.
States have intervened to cover many low-income elderly beneficiaries who were falling between the cracks in their transition to the new Medicare program.
In essence, the two sides could explore two different ways of delivering health care, to determine which is more efficient and popular with elderly beneficiaries.
The law offers prescription drug coverage to all 41 million elderly and disabled beneficiaries.
Its emphasis on private market forces and consumer choice, they say, has made it too complicated for many elderly beneficiaries.