As the reform discussion has waxed and waned, different arguments against the Senate bill framework (individual mandate, set up private market for uninsured to buy in) have been in vogue. I think the most fundamental objection at the end of the process is that an individual mandate limits personal freedom. Of course it does, just as every law ever passed does. You have to decide if the limit of freedom is worth it.
The most popular aspect of the Senate bill is the ban on pre-existing conditions and ending recission (denying cover after someone gets ill due to say there was a pre-existing condition that wasn't disclosed). The individual mandate and the insurance reforms go together. And the general approach of reform normatively assumes that everyone should be covered. This assumption could be based on some notion or morality, or could be more practical. If the uninsured get care eventually, we might as well cover them in a more straightfoward manner. I believe the only way to ever have a hope of controlling the rate of cost inflation is to first cover everyone and end the cost shifting. There are a variety of reasons in this vein.
Republican opposition to a mandate based on limits to freedom is a coherent argument, meaning you could believe such a mandate is a limit of freedom (of course it is, just like every other law), and that this limitation is not worth it. Fine. You will never get to anything near universal coverage without a mandate of some sort, but you could decide freedom was more important than universal coverage.
But this logic should then lead to a denial of care to persons who are uninsured. With freedom comes responsibility. If you are free from having to purchase insurance, shouldn't I be free from having to pay for you if you are not covered? Republicans aren't quite ready to go this far, at least not many of them or those who have to get elected. The hardest thing for them politically is how to appeal to the fact that even persons who don't like mandates like bans of pre-existing conditions. The Republican answer is high risk pools. If you took Republican opposition at their word, you could say their policy is to be opposed to mandates on freedom grounds. But, to say those who are uninsured/uninsurable due to health conditions are worthy of being helped, and their preferred method is high risk pools. This implies a sort of 'freedom with a net' approach in which some are worthy of extra help depending upon the reason they find themselves uninsured.
The biggest problem with high risk pools comes from the basics of insurance. The best way to deal with risk is to aggregate as much risk together in one pool in order to spread/share the risk. High risk pools do the opposite, and put the sickest worst risks together. Even adding more cases of high risk to a high risk pool is not likely to reduce the premiums because risk pooling of anything (health, car, homeowners) works because the healthy (or those who don't crash) subsidize those who are sick (and do crash). Here is a useful entry about the inevitable problems is high risk pools (30 states have them now). They are not only chronically underfunded, but they likely also serve as adverse selection magnets as people forego and wait until they get sick.
It is useful sometimes to pull back from the gory details and think about what you think.