Yes, the consulting agencies or headhunters do just that. They do the day to day work of talking to hiring managers. Then they take their cut either when they place someone full-time or take a cut out of the hourly consulting rate.
It varies from place to place, but in the NYC metro area it is common for companies to only staff up through agencies so there is no chance to go directly to companies unless you know someone inside the company already.
Aren't there services to help with that?