Meanwhile, the remnants of Tropical Storm Lee flooded roads and highways from Maryland to New England, adding to the misery of areas still recovering from Hurricane Irene.
Nate had maximum sustained winds near 45 mph (75 kph) with some strengthening forecast, according to the U.S. National Hurricane Center in Miami. A tropical storm warning was in effect for Mexico's coast from Chilitepec to Celestun.
As of 8 a.m. EDT Thursday, Nate was centered about 125 miles (200 kilometers) west of Campeche, Mexico, and was drifting southeast near 1 mph (2 kph). The hurricane center predicted an erratic eastward or northeastward motion for Nate though the day.
Farther out, Tropical Storm Maria was swirling across the Atlantic with winds near 50 mph (85 kph). A tropical storm watch was in effect for the Leeward Islands of Antigua, Barbuda, Montserrat, Nevis and St. Kitts.
Maria was centered about 760 miles (1,225 kilometers) east of the Windward Islands and was moving west near 23 mph (37 kph). The storm's forecast track called for its center to approach the Leeward Islands on Friday or Friday night.
Also, Hurricane Katia was blowing northward as a Category 1 storm in the Atlantic, passing between the U.S. East Coast and Bermuda. Its winds were near 90 mph (150 kph). Katia wasn't expected to hit land, but was pushing large swells to the U.S. East Coast and Bermuda.
Last month, the National Oceanic and Atmospheric Administration predicted an above-average storm season for the Atlantic and Caribbean. Slightly updating its May outlook, the agency called for 14 to 19 named tropical storms, up from a previous prediction of 14 to 18 storms.