Wait. Something else should pop up or as smorizio said there may be a countdown timer showing the number of seconds available to safely cross.
Go to the light(s) push the button and watch. Crossing times vary and may or may not correspond with the width of the street/number of lanes to be crossed.
That said, no matter what, stop and look before crossing.
Many drivers in the city where I worked ran the lights on a frequent basis. Bicycle messengers and some cyclists in general did likewise. Buses and delivery trucks were a constant hazard.
Drivers regularily made left or right turns into the pedistrian lanes as well - failing to yeild as required.
You may be granted the "right of way" but no guarantees that you will actually get...