The compromise was between far left Democrats and center left Democrats, the Republicans never entered into it. At no point were the Dems who were pushing for this courting or expecting Republican votes, hence the procedural trickery they did in the Senate to pass it, but they did require the blue dogs and other center left Dems.
As for the Republican alternative, it was not to pass an omnibus bill which almost never leads to good results, but to pass separate bills to correct flaws in the system in a more piecemeal and less painful way; a method that would make it easier to make corrections as they arose as well as ensure a better understanding of each individual bill and it's impacts.
They wanted to remove restrictions on cross border insurance purchases (to allow for more competition), they proposed allowing individuals to claim the same deductions as businesses to try and break the employer based system, there was also support for legislation to remove lifetime limits and help people with preexisting conditions and even for leaving your adult kids on your family plan (under certain conditions). Their main issue was that because these were separate proposal and not a blanket catch all bill, people like you either through ignorance (which could be due to the lack of media coverage of these proposals) or simple denial, continually state they had no alternative.