Obama did not compromise on the bill, and he didn't have to, because they had the majority all around. But now they don't have that majority in the House.
This is simply not true. The democrats wanted a single-payer system of nationalized health care for everyone, as pushed originally by the Clintons and outright rejected by the republicans. Obamacare (modeled after Romneycare, which was in turn modeled after a plan created by the Heritage Foundation itself) WAS the compromise. It is a market-based system requiring individuals to purchase PRIVATE health insurance. This is as conservative of a plan of socialized medicine as you can get. Many democrats (including myself) were furious at Obama, Pelosi, and Reid for agreeing to this compromise rather than instituting a true system of nationalized health care. They foolishly thought republicans would support THEIR OWN PLAN. How silly of them. But make no mistake. Obamacare was a huge compromise on the part of the dems in order to get some kind of health care reform passed.
If the republicans should accept that Obamacare is now a law that is untouchable, how has Obama managed to change the law as it was written, going around Congress to do so, 5 times? Two of those 5 times changing major provision. Where did that authority to do so come from?
First of all, Obamacare is not "untouchable." The republicans can amend or dispose of the law through the same democratic process by which all laws are changed. But first, they will need to win the Senate and/or the Presidency, and the way they are going, I see little chance of that happening for a long time. The problem is that they are trying to hold the entire country hostage to blackmail for the changes they want.
Let's see . . . in this negotiation, the republicans are supposed to get a year delay in the ACA, approval of the Keystone Pipeline, elimination of a medical device tax, and numerous other things, and the democrats get . . . what exactly? To keep the government running another couple of months and payment of the nation's debts? Can you even comprehend the ridiculousness of that proposal? That is not negotiation. That is not compromise. That is sheer blackmail and holding the nation hostage for the wishes of a very small minority of tea-party backed ultra-conservatives. That is not how a democracy works. It is tyranny of the minority. And in fact, if the debt ceiling is not raised and the expected ramifications occur, it may very well border on treason. I commend Obama for not falling prey to such underhanded tactics. Every time he has tried to negotiate and compromise with the republicans they have slapped him in the face. It is high time they got some well-deserved fallout for their poor behavior.
As for a well-reasoned answer to the second part of your question, I defer to this article: Tom Graves says Obama has changed the Affordable Care Act 19 times