In today's day and age where if a job is offered and you don't take it immediately there's 200 other applicants that will. I'd ask the new employer when they wanted me to start. If they said, "We need you tomorrow." I'd say, "Excuse me just one moment I need to let the people I'm temping for know that they need to hire someone else." And I'd call them on my cell. You probably won't find out that soon anyway but I'd sure take any full time permanent job offered.
I just noticed that you're in Michigan. Jobs are hard to find there so if you get one, grab it.