I've been 2nd choice twice this year, including at the place where I ultimately accepted an offer. I'll admit that it would have been nice to be first choice, if only for purely ego-driven reasons. Nevertheless, simply getting an offer is hard to complain about. But in terms of negotiating and my dealings with the departments there was no obvious feeling of being second choice. They seemed perfectly content to have the offer fall to me and I never sensed that they were "settling" or otherwise unsatisfied to move to the second choice (though they obviously would have preferred the 1st choice).
Clearly I can't comment yet about how it will influence my experience in the dept, but in my grad program we dipped back into the applicant pool after a failed first round of interviews, yet the eventual hire was always treated as welcome and valuable member of the department (despite being at least 3rd choice). Really, if they didn't like you they would extend an offer at all. And everyone in the department has more to worry about than whether the new Asst Prof was 1st or 2nd choice.
Good luck, btw. If you're into the department I hope you get the offer.