> Iirc they've fought Medicare tooth and nail, even though it's modeled on a republican program.
First, you're thinking of Obamacare, not Medicare (actually, the Affordable Care Act); the narrative you're reaching for is that the ACA is modeled on Republican ideas, therefore the GOP isn't allowed to object to it. Medicare is something completely different, a health insurance entitlement aimed at seniors that's existed for decades.
And even then, neither half of the story is really true, because the GOP is not a monolith. Yes, the Heritage Foundation proposed something vaguely similar in the '90s, and Mitt Romney -- a liberal Republican governing one of our most liberal states -- pushed a vaguely similar plan as well many years ago, but the majority of Republicans disagreed with both on the idea. And even if it was based entirely on an old GOP idea, there's no logical way to therefore decide the GOP can't have problems with this implementation of it, or not believe the Obama administration would be competent to execute it.
Think of it this way. Bill Clinton supported military action against Iraq during his term, and even carried it out. Does that mean no Democrats were allowed to object to George W. Bush's Iraq war, because it was "based on a Democratic idea"? Of course not; the very idea is absurd. Same deal here.