Weight critical air carrier awaiting departure at DCA described conflicting wind reports from ATC vs. windsock observations.

Narrative

Taking off near Runway 19 limit of 144.3 at closeout weight of 142.5 with max power; winds were reported variable at 4 on the ATIS. A query to Tower gave a response of 120/4. Getting to the end of the Runway 19 at the #1 position; it was quite evident that the windsock was not indicating the East wind; but a Northerly wind; and was mostly straight; indicating much more than 4 KTS. Looking back over my shoulder to Runway 15; its windsock was straight out and indicating a North wind as well. Looking to the right; the windsock for Runway 22 was indicating a North wind as well; and it was mostly straight out; and down a bit from time to time. Surmising that the wind was really 360/8-10 KTS; I did not attempt to takeoff. Tower was informed of our predicament. I could only withstand 2 KTS of tailwind. I could gain about a knot with packs off; and if I burned down to the minimum takeoff fuel; I could stand about another 2 KTS; but the actual observed wind velocity was much more than what I could handle according to the performance data as indicated by the three windsocks we could see. Meanwhile; aircraft were taking off and landing. Numerous calls to Tower resulted in the same wind readout: 120/4. A 737 said he could handle the tailwind as he taxied up to Runway 19. That statement verified my observation and was a direct contradiction of the Tower called winds. He then took off. Looking around after some time; we could see that the midfield windsock as to the right of the pole from our vantage point but we could not tell if it was indicating a North wind; or a Southeast wind. We called Tower and asked about the direction of the other windsock on the field and all they would say was: 'all the socks point the same.' I asked more than once and that was all they would say. When asked specifically which way they pointed; all they would say was 'all the socks point the same way.' I radioed back: 'Well; the three windsocks up here are indicating a North wind and you're running a South operation.' After a few more minutes; DCA turned the field around. We took off on Runway 1; packs off; with the windsock indicating a headwind; but the called winds were still 120/4. DCA is too short to be using a tailwind. When all the windsocks point the same; you'd think that common sense would prevail and aircraft would takeoff and land into the wind. As it was; we were 36 minutes in taking off; but we were safe.