This is making the faulty assumption that Obama was able to bring those same people in to play in building the ACA website. The sad truth is that most of the feds that were involved in the development of the website were probably hired back in the Clinton era, if not back in the Reagan administration, and are so filled with hubris that they think they know better than the people they contracted for their expertise.
Imagine what it is like to come in to a project with 10+ years in building websites, just to have your professional advice overruled by someone because they just finished reading "Websites for Dummies" and so they obviously know better. Then imagine going through that at least once a week for the entire time you are on the project.
I didn't work on this project, but I was a federal contractor for long enough to be confident that a large number of the issues stemmed not from contractors working the system, nor from partisan BS, but from incompetent federal employees.