B737-700
Flight Crew Last 90 Days 141
Situational Awareness
Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter CFTT / CFIT; Inflight Event / Encounter Weather / Turbulence
General None Reported / Taken
Human Factors
On downwind for 31L we were given a descent to 2;500 MSL and a heading of 090 (left base). ATC then told us to call the field. I asked the Captain to ask for 2;200 which was the FAF altitude because there was a layer between us and the field. He asked for direct to the FAF and ATC cleared us a 330 heading and told us to maintain obstacle clearance and cleared us for the approach. As I turned to the heading assigned and descended we received a 'CAUTION OBSTACLE' warning. Just before receiving the warning we were able to pick up the field visually. I added power and started a slow climb and turned to the right to stay away from the building. We then continued the approach and made an uneventful landing. We didn't execute the go-around like we should have since we saw the building; only later realizing that that is only the case in day VMC.The clearance was confusing and the heading took us directly into a path towards the building in downtown. I should have squared the base or just asked for the ILS approach.
[Report narrative contained no additional information].
In an attempt to expedite their arrival the flight crew of a B737-700 asked ATC for direct to the FAF and a descent to the FAF crossing altitude.  When ATC assigned a heading to intercept and cleared them to descend as requested; advising they were responsible for terrain and obstacle clearance; their track took them toward a downtown building and a subsequent single EGPWS Obstacle warning was generated.