Illustrator :: Filling A Space

I am doing maps. Bodies of water need to be shaded, i.e., filled with a background. The current problem involves coast lines. I have two bodies of water to "shade" -- Pacific Ocean off California and the northern part of the Gulf of Mexico.
 
I enclosed the Pacific Ocean segment by using straight lines at right angles to intersect the coastline. Use the Paint bucket and no problem. When I go to the same, i.e., enclose the northern part of the Gulf of California by using a straight line across the the gulf enclosing it Illustrator gives grief. Sometime one error message, sometime another, sometimes nothing. I am told to select the paths enclosing the space I want to "Live Paint". I do it, but no joy.