There is no strong evidence that the democrats would’ve delayed opening up the website.
Republicans could have spent the last couple of weeks using all their energy on the website, instead they focused on the shutdown battle which got them nothing. They are now viewed more unfavorably than if they have done nothing at all. They actually somehow made Obamacare more popular when in all fairness it should have been getting slammed for how horribly the website was designed.
While the website is nowhere near fixed, it is functioning a lot better than it was two weeks ago which again is when the Republicans should have made that the main news story instead of the shutdown.
I applaud your enthusiasm for your favorite political party.