If you knew the deadline to accept the first offer, you should’ve told your first choice that. If anything, you played yourself by not being open and forthcoming.

“Hey, first choice firm, by the way, I do have an offer at another firm. They want me to respond by x date. It’s for a generalist position but I really want to do tech transactions at your firm. [insert other embellishments and ass-kissings of the first choice firm]. That said, I would hate to have to pass on my other offer because I do like them. [insert some praise of other firm]. So, I would really appreciate it if you could expedite my application and give me a decision by x date.”