The additional rainfall could cause life-threatening conditions, the NWS said in a bulletin.
The system is crawling north-west at a speed of just 8mph, dumping heavy rainfall as it tracks inland.
Despite the flooding concern, however, New Orleans experienced only light rain and winds on Saturday, and no flooding.
A dry, sunny Monday is expected as Harrisburg area residents head back to work this week, forecasters said, but they warned that pleasant weather will make way for high humidity and possible thunderstorms by midweek.
Elsewhere, the tropical Atlantic is covered with Saharan dust, which we can see in South Florida in the hazy skies.
Still, the storm had not inundated New Orleans as feared.
Late Saturday night, authorities were trying to rescue a family of five trapped by high water in the south Louisiana town of Franklin, according to KTBS-TV.
"Trailers don't hold, no matter what type of storm", Webber said.
At least one levee, in Plaquemines Parish in the state's tip, was already overtopped by water by midday on Saturday.
But officials learned after Hurricane Katrina that some residents wouldn't evacuate because they couldn't bring their pets.
Louisiana's most populous city, New Orleans, looks set to avoid a direct hit from the hurricane - with the worst expected further west near the city of Lafayette instead.
Its heaviest rain on Saturday and Saturday night focused in southern MS and Alabama where up to three to seven inches fell.
"This was a storm that obviously could have played out very, very differently", Gov. John Bel Edwards said. "This is just the beginning", he said at a Saturday news conference.
New Orleans Mayor LaToya Cantrell said Sunday the city was "beyond lucky" that rainfall there fell well short of early predictions of a deluge that could overwhelm the city's pumping systems. The couple, 72 and 70-years-old respectively, walked a mile in the rain from their trailer to a shelter at a Baton Rouge middle school only to be told that they could not bring in their two cats and small dog. Mandatory evacuations were being put into effect for areas south of Highway 317 with sheriff's deputies going door to door to notify residents. "We don't have the resources to stay in a motel for seven or eight days".
By the time the storm reaches Pennsylvania, it likely will be mostly broken up, Travis said.
"Even though Barry is weakening, the threat of heavy rains and the potential for flooding continues from Louisiana northward through the Lower Mississippi Valley", the hurricane center said.
Heating Up Behind The Rain: The clouds and rain from Barry will keep our temperatures in check through the first part of the week, but that changes by the end of the week!
Meanwhile, the remnants of Tropical Storm Barry are crawling their way northward through Arkansas.
The warming world is also making these storms more sluggish.
Barry is expected to turn toward the north-northwest tonight, followed by a turn toward the north on Sunday (July 14), NOAA said.