Okay, first you are saying that the negativity is coming from pundits and papers. That's their job (to be negative). American pundits and papers are no different.
As for real British people, my experience has been that they have a very positive view of Americans, one that is based largely off of movies and TV. America is the land of cowboys and indians, wide open spaces, giant skyscrapers, beautiful tanned beach bunnies, enormous steaks, Disney World, Coca-Cola, Elvis Presley, John Wayne, and Michael Jackson. America is a place that is always sunny and warm. It's a place of great achievements - you put a man on the moon, for goodness sakes!
America is seen as a place without a class system and a place of prosperity. Where I would say that most British fictional television is set around the economic lower class (e.g. shows like Coronation Street, Eastenders, Only Fools and Horses, and the Royale Family), American shows usually focus on financially well off people and even its depiction of people that are not wealthy makes them look wealthy (How much do you think Monica and Rachel's apartment would cost, in Friends?). This gives an illusion of comparative wealth. I remember as a kid thinking that all Americans had ranches like Southfork (Dallas) or penthouses like the Jeffersons.
Where the average Brit might have negative comments to make about America is not the people, but the government. Views there might divide along party lines, but I commonly hear people wondering why America feels the need to butt into everyone else's business and never plays like a good team member (e.g. refusing to sign the Kyoto protocol). When I visited England not long after the Iraq invasion, there was a lot of grumbling that America drug Britain into that mess. But as easily as Brits separate themselves from their government, they see a distinction between the American people and their government and don't blame you.
Brits tend to not understand some of the ways America does things. The shocking level of gun violence and your refusal to address it puzzles them. The lack of a national health care confuses them. My dad likes to say "In America you might have better doctors and fancier machines, but in Britain I never have to worry that if I get sick, I will lose my home. Not having that stress is the best medicine
." (He lived in America for 6 years and experienced the devastation of medical bills). We don't understand why you choose to have such a work/home life imbalance. We don't understand why you are afraid of nipples.
When we meet American tourists, we find you to be a friendly and generous (although extremely loud) people. We don't understand your obsession with having ice in all of your drinks.
The one place where we find you annoying is your obsession with considering yourselves to be the best country on Earth. You aren't. There are no metrics except for things like obesity and prison population where you rank number one. If you started thinking of yourselves as equals instead of betters, then everything would be great! America is a great place to live, but so is Britain, Canada, Italy, France, Germany, Japan and about 80 or so other countries. Stop being the neighbor that has to constantly tell us that their kids are smarter, their car is bigger, and their house cost more. So when the pundits are criticizing, it might not be a bad idea to think they might have a point.