Yes, the supermarkets have average prices similar to the US. Just watch it because some items are much more expensive and some much less.
I assume you will be going out for lunch and dinner quite often as well. Where we spend most money is on dinners and drinks. The prices at bars and restaurants are all over the place just like in the US. Happy hours on food and drinks seem to be mostly on the Dutch side and it does help the expenses if you can catch them.
Some places with decent food and prices or happy hours to the best of my knowledge:
Sublime HH Bamboo House HH Sint Maarten Yacht Club Dingy Dock Bar HH Dingy Beach Bar HH Greenhouse (Simpson Bay & Philipsburg) HH Hubble the Pub Rembrandt's Marie Estates Driftwood Perch Orient Beach HH Buchaneer's Beach Bar