I'd compromise for $12, because then at least it will have kept up with inflation since 1969 - anything less than that, and the American worker has in effect taken a pay cut since then and I don't see why that has to be the case.
I'm also willing to stagger the hike over time, if your concern is the size of the jump in one go - but if we're going to do that, we HAVE to peg the minimum wage to something solid once it gets to where it should be, so that we never have to face this situation again. If we peg it to inflation, that would be great; I say peg it to worker productivity, but I know that's a difficult sell for a lot of people.