Quality over time, longevity of career, influence on the direction of music generally, popularity across the nation and abroad, iconic tunes and iconic performances, a sense of universality to tunes but also reflective of what is uniquely American, not derivative nor regional, not pigeon-holed into a genre regardless of where they started. What American artist fits this best?
The complexity here is difficult because we are talking about a BAND, not really an individual artist. That's where things get tricky, because Bob Dylan, Michael Jackson, Madonna or Prince all have claims. Then there's Elvis or Sion & Garfunkel too.
But personally, I consider Springsteen and the E Street Band effectively a band because of the popularity in the US of Clarence Clemons, Max Weinberg and of course Steve Van Zandt -- clearly hugely influential on Bruce's sound. As such, they'd be number one for me because I think they fit the above criteria best.
Beach Boys are runners up, and pretty close. Very close actually. Their sound is somewhat more regional which offsets how iconic they were. It's near a tie.
To me, Steely Dan and REM are next in some order. After that is tougher, but Tom Petty & The Heartbreakers stand out.
I want to say Lynyrd Skynyrd because I love them so, but they weren't around long enough. CCR is in the top 10 but there's another shortish career. I can make a case for Van Halen or Aerosmith, but I bet I can make as good or a greater case for the Grateful Dead, The Ramones, Metallica, Beastie Boys or Talking Heads despite them all being "sub-culture" bands to some degree.
I leave out The Doors and The Eagles because I've never understood why either are as popular as they are.
Here's one nobody's mentioned yet -- The Cars. For several years they looked like they might be The Next Big Thing. But their geeky leader being super rich and married to a swimsuit model may have truncated their ambitions a tad.