An ERJ-170 flight crew allowed themselves to get rushed when cleared to expedite their takeoff and failed to fly the Nation 1 SID from DCA as cleared.

Narrative

[We were] told to take the runway; traffic 7 mile final. Crossing the threshold of Runway 19 we had just started the before takeoff checklist and the First Officer was off the radios making the 'prepare for takeoff' announcement. We got clearance while he was still off the radio as the Controller wanted us to expedite the takeoff. The First Officer came back and I told him we were cleared for takeoff. He read back the takeoff clearance; which was to fly the National 2 departure; i.e. fly the DCA 185 degree radial up to 5;000 MSL; and then expect vectors. As we rotated I called for NAV instead of heading as I never saw the FMS extension of the DCA 185 radial. I turned around 700 MSL to intercept the course to HAFNR. My First Officer asked ATC if we had a heading to fly and he said not yet; 'don't worry about it; fly heading 300.' We complied and were cleared direct to HAFNR and up to FL200.I advocate more in depth preflight briefings about departures. They become so standard that we tend to shorten them in our briefings.