It's a strategy that is proving time and time again that it doesn't work that way, Obama tried it time and time again,
The thing that raised my eyebrow about this was when the original Affordable Care Act was proposed and Republicans immediately dismissed it as "too-left" which was kinda hilarious given that I recall either the BBC or Guardian (I'll try and look for a source later) stating that to the UK Conservaties the original ACA was too-right...too-right for a British conservative party. So of course, Obama complied and revised it, complying with the Republicans to pass a watered down version (or a WATERED watered down version depending on how you look at it) and cut to today where the GOP have just flat out said that they never agreed with it and they'll get rid of it immediately. Effectively neutralising something that could've greatly benefited people.
Also, one other thing. Why did the Obama administration/Democrats put up with the term "Obamacare"? Wasn't it a term coined by the right and/or Fox News? Instead of correcting the term did they simply adopted it? Terrible idea if you ask me.