According to the Playbill article, an extension doesn't seem likely.
"A wave of enthusiastic reviews for Broadway's A View From the Bridge prompted "close to $500,000" in box office sales on Jan. 25, the day after the revival of Arthur Miller's drama opened at the Cort Theatre.
The box office boost and the raves don't necessarily translate to an extension, however. A spokesperson told Playbill.com that the closing date of April 4 is firm. A limited 14-week engagement was planned. The Cort is already pre-booked for an April 14 launch of a revival of August Wilson's Fences.
The New York Times reported that co-star Scarlett Johansson has a film commitment in the spring."
A View From the Bridge