The Mets did once throw four consecutive shutouts, including three against the Phillies. It was in 1969, with Gary Gentry winning twice in that span (there was a day off) and Jerry Koosman and Tom Seaver winning the other two.
Interesting that the first of those four was the night the Mets clinched their first division title, a 6-0 win over the Cardinals. Of course you know that Joe Torre made the final out.
Tonight, they have a chance to match that with their ace, Johan Santana, going against Milwaukee.