Date: 201503
Local time of day: 1201-1800
Location: LGA.Airport, NY
Flight conditions: VMC
Light: Daylight
Aircraft: EMB ERJ 190/195 ER/LR
Operator: Air Carrier
Operating under: Part 121
Flight plan: IFR
Mission: Passenger
Flight phase: Taxi
ATC / advisory: Tower LGA
Reporter organization: Air Carrier
Reporter function: Captain; Pilot Not Flying
Reporter qualification: Flight Crew Air Transport Pilot (ATP)
Human factors: Situational Awareness; Communication Breakdown
Second reporter function: Pilot Flying; First Officer
Anomaly: ATC Issue All Types; Deviation / Discrepancy - Procedural Published Material / Policy
Detector: Person Flight Crew
When detected: Taxi
Result: General None Reported / Taken
Contributing factors: Human Factors; Procedure; Weather
Primary problem: Ambiguous

Narrative: LGA had reported winds of 310-330/27 and changed departure runways from 31 to 4.  The winds were within the aircraft limits and we taxied out with our fuel of 12.7.  When coming around by taxiway foxtrot; ground told us to contact tower and that we were #4 for departure so we decided to start engine 2. Once on tower we heard the reported winds 330/28G34 which is now outside the aircraft limits.  We asked the tower to please 'say the winds' again and he again said 310-330/28 G34.  We told him that was outside our limits and we would need runway 31 and he sent us back to ground.  Ground had us cross RWY 4 taxi via AA and then cross 4 again at taxiway G.  He told us to taxi via B to 31 and we were #1 for that runway.  We left both engines running based on that.  Once asking about a new climb out he told us since we can't conform with LGA departing runway there would be a delay and he'd get back to us with a climb out.  The company aircraft behind us had to do the same and asked how long the delay would be for fuel planning purposes and he didn't know.  We were going to shut down an engine since we were at approximately 12.3 and take-off min was 12.0.  As we were about to do that Ground came back said to start engines if we shut them down; gave us our climb out and said we were # 2 for departure and go to tower. We switched to tower and went 'below the line' and at that time our fuel was 12.2.  While waiting to line up the tower continued to release aircraft off of 4 and when we inquired he then told us he had to get the six other aircraft off runway 4 before we could go. We lined up on Runway 31 and took off with fuel actually slightly below min. at 11;980Due to delays from tower and not keeping us 'in the loop' of releasing other aircraft first; and we only had 600 pounds taxi fuel.  I would've called to get an amended release for fuel since burn was approx. 4;000 pounds to BOS but being told I was going to be airborne and be within fuel limits I didn't think it was going to be a factor.It doesn't take much to get 'in trouble' at LGA either taxiing or getting holds coming into LGA.  It would be a good idea to keep things like this in mind when having flights going into LGA especially when there is weather or high winds to have some additional taxi fuel or holding fuel when flying into LGA.


Second narrative: We watched the fuel and knew it would be close to [minimum takeoff fuel]. I asked the Captain about getting more fuel but he said we could actually take off with less than [minimum takeoff fuel] according to something he had read previously.


Synopsis: An ERJ-190 flight crew reported departing LGA with less than minimum takeoff fuel because of weather and ATC complications.