It's a stretch to think that a functioning mobile app on election day would have made the difference between Romney winning and losing. The election wasn't really that close. And I say that as someone who voted for him.
It's not a stretch to think that a functioning GOP GOTV campaign could have made the difference in 4 swing states that tipped the election to Obama (CO, FL, OH, VA), where the vote differential was just under 400,000.
Romney had 37,000 field volunteers, plus phone bank. I don't know how many were in each of the four tipping point states, but had each of them been able to bring in between 10 and 20 voters who didn't vote (of the 2 million extra who voted for McCain in 2008 but were absent this year), Romney could have won.
Instead it sounds like due to the massive Orca failure, they all gave up and went home.
(and fwiw, I say this as someone who voted for Obama. Not sour grapes here, just assessing the IT project failure.)
The result of Davies fieldwork in UK elections showed that active local party activities (including GOTV) can be worth up to a 2%-4% swing - this is from an election where 2nd generation electoral computing systems were used.
In Scotland we have 3rd generation systems (one system for all elections vertically, local government, Scottish Parliament, Westminster Parliament, European Parliament, and horizontally, 2011, 2008, 2007 back to the 80s).
The US parties be roughly considered as having 2 and half generation systems, so you might expect a difference at the top end of that.
I don't follow US elections that closely but you can work the numbers out.