The plan:

July 27, 2013 WordPress 3.7 announced.
July 28, 2013 Kick-off at WordCamp San Francisco Hack Day.
August 7, 2013 Initial meeting to scope out the release. See this post and this one.
Week of Sept. 16, 2013
September 28, 2013
Beta 1. At this point, development of new initiatives (updates, language packs, etc.) should be complete.
From this point on, no more commits for any new enhancements or feature requests in this release cycle, only bug fixes and inline documentation. Any enhancements/feature requests not completed and committed by this point can be resumed in just a few weeks at the start of WordPress 3.8.
October 10, 2013 Beta 2.
Week of Sept. 30, 2013
October 18, 2013
Release candidate 1.
Week of Oct. 14, 2013 Week of Oct. 21, 2013 Target date for release of WordPress 3.7.

To get involved in WordPress core development, head on over to Trac and pick a 3.7 ticket. Need help? Check out the Core Contributor Handbook.

Get your patches done and submitted as soon as possible, then drum up people to test the patches and leave feedback on the ticket. As stated above, no patches for enhancements or feature requests will be committed after the posted deadlines, so that we can all focus on squashing bugs and hopefully deliver the most bug-free WordPress to date. Wish us luck!