We cherish the resumes we get and if we have a job that might match, we'll call within two to three days of receiving the resume. We keep names on file that we think we might have a match for, sometime. Tell them to be sure not to send your resume to your current employer by accident. It has happened. You can work with more than one recruiter, but be honest if a recruiter asks if you're doing so.
Some companies give more than one contingency firm the chance to find a candidate.
Retainer firms generally get an exclusive for any job search. Don't discount search firms outside your geographic area, even if you're not interested in relocating. Many firms like Battalia Winston International have offices in several locations and are retained to fill jobs all over the country. Check back periodically with a headhunter you've met or talked with if you become interested in switching and haven't heard from the person in a while. Just don't hound them.