Universal healthcare was proposed by Teddy Roosevelt in 1912, but the debate really got started in 1953 when Truman introduced Medicare (which took another 12 years of debate to pass). Clinton revived the debate in 1973, but was royally trounced and so they've been chipping away at it until Obama said it was his #1 priority.
So. Originally, the medical lobbies and the Republicans who favor private and oppose government services were able to quash it by arguing that everyone could get insurance privately with Medicare and Medicaid filling in the gaps. But now it is so expensive that it ruins many large companies like GM and many small businesses who are the core of their constituencies, cannot offer insurance. An increasing number of middle class Americans are becoming uninsured. Even the medical lobbies agree that reform is needed. Insurance companies are willing to offer coverage to everyone without exclusions if everone has to be covered.
At the extremes, many conservatives really just want to kill any plan at all and many liberals would rather dispense with private insurers entirely and offer medicare to everyone of all ages.The current debate is how to cover everyone, while (as Mimi says) trying to piss off as few people as possible.
Currently, Democrats want a 'public option' insurance company to compete with the private insurers. Republicans are afraid that it will take over the system and hope to embarrass Democrats by killing their plans. See these links for some more information on their positions.