The show didn't do well, but had a respectable run for a flop, 174 performances. Having said that I enjoyed the few songs I saw, there's a certain sameness to them, and I have no idea how the book was. So, maybe the whole show didn't work as well as some of the songs. But clearly a run of 174 performances suggests there was enough word of mouth to keep it going for that long. And perhaps it was just a case of not being a premise that fit enough audience's idea of what they wanted to see.
The score is by By Alan Zachary and Michel Weiner. I don't know their work, but if you've ever taken a Disney cruise, they wrote the show Twice Charmed that's performed there. The book of First Date is by Austin Winsberg, who wrote for Gossip Girl, and did the adaptation for last year's live The Sound of Music on NBC. From what I can tell, the story pretty covers what the title says -- following these two characters on their first date, involving their friends and memories of past dating disasters.
(I posted a video with Zachary Levi a while back where he sang in a joint-venture between the National Park Service and the Muppets, and he's quite a good musical performer. If you missed it and are interested, you can see it here.)
This is the second number in the show, "First Impressions," made from the recording session.