Edward Snowden's revelations about a vast American data dragnet may have riveted the world for weeks, but in the United States the fugitive and his scramble for asylum are overshadowing the substance of the leaks themselves.

US broadcasters last month gave wall-to-wall coverage to the bombshell leaks by Snowden, a former National Security Agency contractor who spilled classified information about NSA counter-terrorism programs.

But the networks and cable news operators soon bumped the NSA story from the top news slot in favor of the closely-watched Florida murder trial of George Zimmerman, who on Saturday was found not guilty.

In Congress, US lawmakers swiftly convened public and classified hearings last month to assess the programs that scoop up billions of pieces of telephone and Internet data from Americans and others around the world.

But after a flurry of bipartisan denouncements of the leaks, and some calls by lawmakers to revisit the authority Congress bestows on the NSA and other intelligence agencies, the House and Senate returned to executive nominations, debates on student loan interest rates and a farm bill.

Proponents of reform of the surveillance programs worry that the saga of Snowden, who has eluded US capture for weeks while holing up in a Moscow airport transit terminal and who on Tuesday requested asylum from Russia, is muscling debate about surveillance policy out of the US headlines.

"That is a concern. Snowden himself and his travels now, his asylum, have become sort of the salacious part of the story that the press is interested in covering," American Civil Liberties Union legislative counsel Michelle Richardson told AFP.

While Richardson agreed that US media has covered "the substance of the case," the twists and turns of a man desperate to avoid facing charges of espionage are driving the story.

"The media has been paying far too much attention to the person behind the leaks, and that's unfortunate when we're talking about what we can do to fix these problems that he's exposed," said Trevor Timm, an activist with the non-profit Electronic Frontier Foundation.

Some lawmakers have introduced bills aimed at recalibrating US laws on surveillance, but this summer and autumn will be spent on more pressing issues, such as a looming clash over the US budget.

Privacy experts are focusing on the secret court set up under the 1978 Foreign Intelligence Surveillance Act (FISA) to handle requests for warrants against terror suspects.

The court's powers were broadened after the terror attacks of September 11, 2001, and the court is seen as secretly authorizing the NSA's data collection.

A bipartisan group of senators has introduced a bill urging President Barack Obama's administration to declassify key FISA court orders and White House interpretations of post-9/11 intelligence-related law.

"The administration can offer oversight and transparency reforms to these surveillance programs," Timm said.

But many Americans seem ambivalent about a profound questioning of NSA powers.

According to a recent Quinnipiac survey, 45 percent of Americans believe US counterterrorism efforts have gone too far, against 40 percent who do not.

But 51 percent support the gathering of telephone metadata -- phone numbers, locations and other information, but not call content -- in order to help thwart terror attacks.

Is such a program therefore necessary to ensure the safety of Americans? Yes, according to 54 percent of respondents. Is it too intrusive? Nearly the same number, 53 percent, said yes.

The debate could crystallize when Congress renews authority for the programs -- in June 2015 for the telephone data collection, and December 2007 for PRISM, the program which monitors Internet and email use.

"Hopefully we will have had enough debate and hearings and investigation so that at that time, we will get meaningful reform, and it will be very difficult for Congress simply to reenact the law as it now stands," said Sharon Bradford Franklin, senior counsel for The Constitution Project.