In our area it is usually a minimum of one week but much depends on whether they have a vacant room. They may argue they need such time to get to know the person. One of our homes has a room set aside so its worth asking.
Hi there, I use a care home that will do anything from day care, one day overnight respite through to full time residential. I actually found two homes that would do that, although finding homes that would even take my Dad (he's 60) was hard enough.