Well, if people actually got together and ironed out a good plan, we'd be in good shape. Personally, I think a single-payer system should be handled by a private company given a government contract which must be renewed every 5 years or so (judging by the fact that it's taking me over 6 months to apply for Navy OCS due to paperwork slowness when it really ought to only take 2 makes me uneasy about how the government would handle healthcare). Unfortunately, there is just too much money involved with our current health care business that just makes a good, working solution impossible.
EDIT: I did not mean to imply that there were no copays or deductibles in government worker insurance plans. It is, after all, ultimately a private insurance company that you deal with. I simply meant that the plans provided are often much more comprehensive than the average person gets working for Company X, and the out of pocket expense is lower. You're also covered for life after retirement, which most companies don't offer. If you needed knee surgeory tomorrow, for whatever reason, you'd have a much easier time with your insurance company than most. That's all.
The flip side, as someone pointed out, is that military jobs are much more dangerous, so you could argue that they deserve it.