Flight crew awaiting departure at DCA reported almost encroaching on Runway 15 while taxiing to Runway 19.

Narrative

During taxi out for Runway 19 at DCA there was a long line awaiting departure. Assigned to Taxiway 'J'; hold short of Runway 15. With just over 5K fuel scheduled for arrival at our destination; decided to shutdown #2 engine until closer to departure. The aircraft ahead was cleared to cross Runway 15 but since we were still on one engine; we elected to remain in our original spot on Taxiway 'J'. After waiting approximately 5 minutes; we were cleared by Ground Control; '...to taxi to and hold short of Runway 19.' We were NOT given any clearance to cross Runway 15 but didn't think about that relatively new requirement. Still; we queried ground as to our clearance and was again told to; 'taxi to and hold short of Runway 19.' As Captain added power to begin taxi I noted an aircraft on what I believed the River Visual for Runway 19. We started moving toward the Runway 15 Intersection and as we got fairly close I commented to the Captain that it appeared the aircraft on final was actually landing on Runway 15. As he began to brake ground told us to hold short Runway 15; which we did. In retrospect we should have questioned his original clearance to Runway 19 but old habits about; 'taxi to Runway xx' die hard. In addition; we were TWICE told to taxi to Runway 19 with nothing said about Runway 15. Had we been on two engines and been able to accelerate to taxi speed faster; we may have crossed the Runway 15 Intersection and; at the very least; caused the approaching aircraft to go around. Ground did recognize and apologize for the confusion before turning us over to Tower for departure.