It depends. If you're shopping at Whole foods you can pay with card. If you're shopping at the bodega you pay with cash because the processing fees are larger than their margin (and consequently they might not have the card infrastructure).
This is person to person. I buy stuff from the bodega a few times a week. I use my card because that's my preferred payment method. I never carry cash around. I wish they, "made" the same off me either way but it's not really my fault that it costs them something for me to pay in a convenient way.
To be fair, credit cards in the US can have great rewards, probably better than in any other country. I get 2-5% back on all of my purchases, which means that the credit card fees paid by the merchant aren't really "wasted" on the payment processers.
In big cities at least. I used cash once in the last three months I think (because the place we were shopping at looked a bit dodgy).
You can generally get by in most suburbs that way as well. I really only use cash for my monthly D&D game when we're buying take out.
I live in a small (300,000 people) Midwest city and I pretty much only use cash for person to person transactions.