can you post sql used to create the table?
A multicolumn index on user and password might help:
alter table tablenamehere add index user_password (user, password);
Or even just an index on user
alter table tablenamehere add index(user);
- or -
alter table tablenamehere add unique index(user);
to force unique user name if you don't already have that constraint in place.
This would help mysql to organize by user name, your primary key is only organizing by id, which doesn't help when it comes time to look up by their name.