Ehh, in the US there's a 'general consensus' accent. It's considered rather plain, compared to unique dialects, like Southern Dialect, which aside from 'Ya'll' I don't use many Southern colloquialisms, courtesy of a mother from the North. ( I admittedly find Southern accents to be 'bumpkin'.)
I guess I can't really comment on the situation in the US: as an onlooker, if I can't isolate a particular flavour of US accent it's just "generic American" to my ears, but I figured to someone living there, everywhere still has its own regional accent, much the same as tends to be the case here (edit: clumsily worded, I guess that's what happens if I post at 5:30 in the morning...)
Living in the UK, my experience has been that there's a fairly direct correlation between a person's insistence that they have no accent and my difficulty understanding them! A "standard" accent may be considered to be whatever a typical BBC newsreader speaks in that their speech is somewhat contrived for mass ease of understanding, but it's still definitely an accent, usually south-eastern but at times from other areas such as Wales; but that leads people with similar accents to then conclude that they speak likewise, often with assertions of unaccented clarity, when that's really not the case. I remember living in Hertfordshire for many years, an area where I frequently encountered this "I speak standard, unaccented English" phenomenon, but I never entirely got to grips with the local accent: I often found myself having to ask people to repeat themselves, which seemed to irk some of them as they considered that repeating oneself was my job!