ESPN's Adam Schefter and Chris Mortensen are reporting that the "growing belief inside league circles" is for a new CBA to be agreed to sometime in the next seven to 10 days. While nothing would become official immediately, the plan, according to this report, would be for the deal to be ratified on July 21 at the owners meetings in Atlanta. (So much for Detroit hosting them this month.)
The past two weeks, July 15 has been mentioned as an important deadline for the negotiations, partly because the new CBA wouldn't go from unofficial to official just like that. It will take time to get everything in order and to have it ratified by the owners/signed off by the players, which is why the hope is for something to be agreed to by the end of the week. That would give everybody time to plan for the end of the lockout, which would happen on July 21 under the plan where the owners ratify it in Atlanta.
While July 21 is probably a much later end to the lockout than most were hoping, it would allow all 32 NFL teams to open training camp on time. The Bears and Rams are scheduled to open camp on July 22, so it would be quite the time crunch for both franchises, but at the very least they would be able to get together and prepare for the Hall of Fame Game on August 7.
The rest of the NFL would have a week or so to get things in order before camp opens.