Here's a brief excerpt from Loren Gross's excellent UFOs: A History Volume 1: 1947 detailing just how quickly the press release was "deflated":

[...]

Bedlam.

Washington was caught flat-footed. So many reporters jammed the Pentagon press room one would think money was being given away. Lt. General Hoyt Vandenberg, Vice Chief of Staff, Army Air Corps, dashed to the press room to take charge personally and bring some order out of the chaos. Fending off the pad and pencil boys, General Vandenberg got Fort Worth, Texas, Eighth Air Force Headquarters on the phone and conferred with the officer in charge, Brig. General Roger Ramey. Nearly every major American newspaper, plus some foreign ones, tied up the phone lines to the Roswell Sheriff Office of George Wilcox. The San Francisco Examiner, however, correctly surmised that the Commanding Officer of the Eighth Air Force was its best bet and got through just ahead of its competitors.

After Vandenberg hung up, General Ramey made himself available to the press. The San Francisco Examiner, a Hearst paper, was the first to get through to the General. The Examiner found General Ramey in a seemingly jocular mood whose first words when picking up the receiver were: "Everybody in the country is trying to get through on this telephone." His statement on the saucer matter was less sensational than those coming from Roswell. The fragments, General Ramey said, were "flimsy," of a foil construction of some sort. The General had the word of Warrant Officer Irving Newton, the Fort Worth Air Base forecaster, that the thing as only a beat up weather balloon radar reflector. The Fort Worth commander expressed his consolations that he had to disappoint the news media by stripping the saucer find of its glamor.

The tumult had lasted an hour.

After the capture story had swelled and then burst like a bubble, military officers at Roswell Field received, according to sources known to United Press, a "blistering rebuke" from Air Corps Headquarters in Washington for their part in the panic.