Often, this claim concerns what is called "deep gas" offshore in the Gulf. For example, from here.

Trapped more than 15,000 feet within the earth's crust, so-called "deep natural gas" represents a tremendous untapped domestic energy resource. Government studies estimate that there could be more than 20 trillion cubic feet of untapped deep natural gas deposits in the Gulf of Mexico-- about as much as is currently being produced from all areas in North America on an annual basis!

... Unfortunately, despite significant advances in deep gas technology, these prospects remain very challenging to find and develop successfully. Since 2001, Gulf natural gas production has decreased from 5,128 BCF to 4,175 BCF in 2003. Deep gas discoveries may help reverse this trend however: deep gas production increased from a relatively low 284 billion cubic feet in 2000 to 421 billion cubic feet in 2002.19

At this time and for the foreseeable future, most of this gas, if it is indeed there, is still effectively "stranded" despite what articles like Oil companies going deep in Gulf of Mexico drilling say. I would pay more attention to facts like this one, from the lastest ASPO-USA newsletter

Canadian gas production peaked at 17.4 billion cubic feet a day in 2001 and 2002, according to figures from the Canadian Association of Petroleum Producers. Large new discoveries of natural gas have become rare.

Other claims involve the western part of the Gulf nearer to Florida (dry holes and "sour" gas H2S) and completely unsubstantiated assertions about offshore California and the East Coast.

In other words, don't believe everything you read.