I consider the Heritage Foundation to be a conservative think tank, and they do as well. Believing them not to be is an issue you have with your definition of conservatism.
Single payer is a better option, but since it would fundamentally change how health care operates in this country, it's going to take a large majority of the country to be on board with. Single payer would have gone down in flames if Democrats had tried to pass it in 2009/2010. I think they were aware of the political reality that it would be a huge mistake to destroy a private industry and replace it as a federal one without having some real bipartisan support. Being against a single payer system in 2009/2010 was more of an understanding of the political landscape than being against the idea of single payer itself.
At this point, Obamacare is a train moving at close to full speed. Delaying it completely would cause a massive more number of issues than the website is creating right now. For coverage to start Jan. 1st, you have to sign up by Dec. 15th. Open enrollment for the year ends on Mar. 31st. If the website issues continue, I could see the Mar. 31st date be pushed back which is a reasonable solution instead of pushing back the mandate itself.
Boehner broke the Hasert rule to end the shutdown, which he said he would never do. If his power has increased, it's because the Tea Party's power in house has decreased. They were fought off within the GOP since they are mostly responsible for this mess and it's political repercussions. I do think the ultimate deal will be a replacement of the sequester with smarter cuts since the sequester was never intended to actually go into effect. Any total cuts more than the sequester is probably going to require revenue increases and since I doubt that's going to happen, we'll probably end up at a final spending level near the current level but with smarter cuts.
Its the second time he broke the Hasert rule. He did it the last time the Republicans played games with shutdown/debt ceiling.