Approximate time frames for US postdoctoral application decision making and starting
Most postdoctoral positions in the US are made available by individual professors within their own research groups. Consequently, there is no standard timeline for postdoctoral applications, outside of special programs where positions are sponsored by entire departments or institutions.

In general, though, I think that positions are held open at least as long as is required by the guidelines of the individual institution where the postdoctoral associate will be housed (anywhere from two weeks to 60 days), although this may be extended if no suitable candidate is found in the initial advertisement process. 

Moreover, the start date is usually somewhat flexible, but is also dependent on funding—usually people will want the postdoc to start as soon as is reasonably possible.

On the whole, however, if you're applying for an individual postdoc position, I would normally assume that you'd hear back from the postdoc advisor within a few weeks if there's any interest.