A report from the Commonwealth Fund showed that those elderly patients who use Medicare are most satisfied with their healthcare offering.

Fewer than 10 percent of those with Medicare said they felt their plan was poor or fair, the report showed. In addition, one in five of those with a policy through their employer said the same thing. In addition, close to 25 percent of Medicare patients did not receive necessary health care, which was lower than 40 percent of patients with employer plans who reported this.

"Policies designed to move the elderly out of Medicare and into private plans need to be carefully designed, so as not to expose beneficiaries to the poorer access to care currently experienced by many working-age adults with private insurance," said Kristof Stremikis, senior researcher at The Commonwealth Fund.

Those people who are still unhappy with their government-sponsored health insurance policy may want to look for other private options. There are many plans with affordable health insurance rates online that could help them get a less expensive policy. Comparing options with current coverage plans could help these consumers.