Obama also declared a state of emergency for Massachusetts.
Like several neighboring states, Maryland could see as much as a foot of rain in some areas -- a major reason the state has declared a state of emergency.
Besides flooding, strong winds are expected to cause significant power outages. The Baltimore Gas and Electric Company, for instance, says several hundred thousand customers could be affected.
Public schools in Baltimore, Montgomery and Prince George's County will be closed Monday.
In the coastal city of Annapolis, city crews distributed sandbags to residents and businesses to help them prepare for flooding.
President Obama declared a state of emergency in Maryland on Sunday.
Sandy could bring winds of up to 60 mph and dump 2 and 4 inches of rain to parts of the Granite State -- likely starting Monday, Gov. John Lynch's office said.
"While the exact path and severity of the storm remain uncertain, it is clear New Hampshire will experience a significant weather event and I urge everyone to be prepared," Lynch said.
New Jersey was the first to announce mandatory evacuations. The state's barrier islands from Sandy Hook south to Cape May must be cleared out, along with Atlantic City's casinos.
"We have to prepare for the worst here," Gov. Chris Christie said. Tolls have been suspended on the northbound Garden State Parkway and the westbound Atlantic City Expressway so people in those areas can leave more quickly, he said.
All state offices will be closed on Monday, with only essential employees expected to report to work, Christie announced.
New Jersey Transit came to a halt and will remain suspended indefinitely.
New York City's ubiquitous public transit system shut down ahead of Sandy's landfall, leaving iconic sites such as Grand Central Terminal and Penn Station empty.
The city expects a slow surge of water to flood low-lying areas such as Queens, the Bronx and Battery Park in Manhattan, Mayor Michael Bloomberg said.
Mandatory evacuations are in place for parts of New York City. Evacuation centers have been opened in 76 locations, and schools in the city are closed Monday.
Offices at United Nations headquarters in Manhattan also will be closed Monday, as will the physical trading floor of the New York Stock Exchange. Operations will continue on the company's electronic exchange.
The Broadway League canceled all Broadway performances Monday night, citing the suspension of public transportation.
Instead of tourists and theater fans, piles of sandbags lined Broadway.
Gov. Andrew Cuomo directed Army and Air National Guard members to mobilize for Sandy, and Obama has declared a state of emergency for New York.
Strong winds and rain that fell sideways lashed the Outer Banks as the outskirts of Sandy pummeled the barrier islands.