I have read stories that it was so hush hush that people didn't know what they were working on till after the bombs dropped and they read it in the papers. I have also read that it was infiltrated by spys who took everything but the kitchen sink back, knowledge wise, back to their government. So who knew?
At least in some quarters, it was not very secret at all. Soviet intelligence, particularly the NKGB and the GRU had recruited a number of agents in place working within the Manhattan project among the scientists who provided the Soviets with detailed information about the research and design of atomic weapons.
The most famous was perhaps David Greenberg, who was part of the Rosenberg ring, but other scientists with night lives as Soviet agents include:
Klaus Fuchs a German born physicist working on the uranium enrichment aspect of Manhattan in 1943.
Theodore Hall, an American who provided comprehensive information about plutonium and the 'fat man' bomb.
George Koval, a Soviet emigre who worked as a radiation specialist and as an officer with the GRU at the Oak Ridge labs
Alex May - A British scientist who actually supplied samples of radioactive material to the GRU.
sources: The Haunted Wood: Soviet Espionage in America by Allen Weinstein
Venona: Decoding Soviet Espionage in America by John Earl Haynes and Harvey Klehr