Editor's note: As of April 27, 2018, there is now a four-month deadline for each proposal's Definition and Commitment phases. The clock is reset once the proposal finishes each phase. This is because sites whose proposals tended to spend longer times in these phases tended to result in closed sites.
Long after this post was originally made, there was an unofficial policy of closing proposals that spend more than one year in Definition or Commitment, but enforcement was completely manual; in mid-2015, it was made automatic.
There is currently no plan to put a time frame on a site proposal. We want to make sure that sites have all the time they need to develop properly. That can happen very quickly for a mainstream site. It might take longer for smaller sites. Smaller sites need time to reach out to experts and develop a following.
There may be some practical point where there has been absolutely no activity on a proposal and it gets deleted as a matter of system maintenance. But there's no "time limit" to get everything through in under "X" period of time.