I regularly travel to the US from LHR with 2 bags. The smaller, laptop-type bag gets squished inside the larger, but within carry-on restrictions, bag untill I'm through security on the way out, then just gets carried loose. Never had any problems actually taking 2 bags onto the plane.

Coming home, the two bags stay separate, and have had no problems taking them through security @ IAD, EWR, BOS, PHL, RDU, LAX, SFO...