Portions of 11 states were under flood watches that extend as late as Thursday, with generally 2 to 6 inches of rain predicted from the central Appalachians to New England.
Heavy rain already was pooling in parts of North Carolina and Virginia.
In High Point, North Carolina, a city of about 100,000 people, streets and a parking deck were flooded, with water rising up to the top of the vehicles' tires.
A man was rescued from his car after water stranded him at a High Point intersection, CNN affiliate WHGP reported
A flash- flood warning also was in effect for the Martinsville, Virginia, area. In Woolwine, high water washed away a 94-year-old covered bridge, CNN affiliate WDBJ reported.
Widespread heavy rains were expected to develop along a cold front that was pushing toward the upper Ohio Valley, central Appalachians and the northern Mid-Atlantic areas. The rain are expected to shift north and east Tuesday night into Wednesday, CNN meteorologists said.
Flood watches were in effect in North Carolina, Virginia, West Virginia, Maryland, Pennsylvania, New York, Connecticut, Massachusetts, Vermont, New Hampshire and Maine.
The weather on the North Carolina coast this weekend could be influenced by Tropical Storm Joaquin, though forecasters at the National Hurricane Center have "very low" confidence in predicting the storm's future path.
As of Tuesday afternoon, Joaquin was pushing west toward the Bahamas, but it is possible it could turn sharply well before it gets to the islands. Then, as Joaquin travels north through the Atlantic, it could strengthen and become a hurricane, the center said in a discussion posted on its website