Given Obama's lukewarm popularity going into 2012, Romney could certainly have won had he simply run a better campaign devoid of fatal gaffes like "47%" and "binders full of women." Romney gave a great performance in the first debate and for a time was tied with Obama in the polls, but again his PR issues not to mention his inability to respond to the Democrats' attacks on his business record did him in as a candidate. Without these mistakes, it's plausible to think that come January 20, 2013 America would've had its first Mormon President.
Undoubtedly, a Romney victory in 2012 would've unleashed a whole host of butterflies. Trump would likely not have run in 2016 if a Republican were President, and even if he did he'd probably lose to a unified GOP establishment. (A big reason he won in OTL was because the Republican establishment was divided between something like 15-16 other candidates.) Without Trump and with Romney, the GOP would be a bit less hardline but still sharply divided between the centre right establishment and far right grassroots.
As for the Democrats, they'd be demoralized four years early. Whatever decision they eventually make in 2020 - to remain centrist or go left - would've already happened by now. A one term President Obama would be viewed much like Carter or Hoover: someone who had good intentions and respectable accomplishments, but ultimately failed to solve the fundamental problems America faced.
That said, it's unlikely that Romney would've gotten anything done as President. Congress would still be divided between a Republican House and a Democratic Senate. Any attempt to repeal Obamacare would fail as it did under Trump; in fact in this ATL scenario Romney would be viewed as less successful than OTL Trump as he wouldn't be able to pass tax reform thanks to Democratic obstruction. If he pushes for intervention in Syria the Democrats would block him, if he pushes for TPP that would die too. Going into 2016, which would still be a year in which an angry electorate wants change, Romney would be deeply unpopular and he'd probably lose to any Democrat. In short, Romney would've been a failure. But America would've made some symbolic progress having elected a Mormon President, not to mention that Trump and his combination of right-wing populism and cronyism would not have come to pass.