Public schools in Providence, the state capital, will be closed Monday.
Obama has declared a state of emergency for Rhode Island.
Radar showed heavy rains from the fringes of Sandy pelting much of South Carolina's coast, from Charleston to Myrtle Beach.
The Palmetto State is expected to avoid a direct hit from the storm, which is expected to make landfall well to the north.
Virginia was one of several states to declare a state of emergency ahead of the storm. Computer models predict parts of the state could see as much as a foot of rain.
Sandbags piled up inside restaurants in the Old Town section of Alexandria, along the banks of the Potomac River.
The Virginia National Guard was authorized to bring as many as 500 personnel onto active duty.
All public schools in Fairfax County, a large school district in northern Virginia, will be closed Monday and Tuesday. Schools in Arlington, Norfolk, and Newport will be closed on Monday.