When NBC broadcasts the parade, they stick to the outdoors. And when presenting a number from a Broadway musical, they either have the stars sing from their float, or let the cast perform from a "spotlight" area if it's a production number. CBS handles things differently -- they keep a theater at their disposal and often cut away for lengthy productions.
And that's what they did for First Date. So, we get to see a couple of songs on stage. The first features the small company and is, I believe, the opening number from the show. It's followed by the two leads, Zachary Levi and Krysta Rodriguez.