The figures are listed below in order of most cap space to least cap space:
For the sake of reference, I'm also listing them in alphabetical order:
As can be seen above, the Giants are $132,418 under the cap as of today. This ranks them 31st in the entire league. Only the Rams have less cap room than the Giants do (they are only $17,718 under the cap). If only one more player goes on I.R. for the Rams, then they'll have to make more room under the cap.
If the Giants sustained another two injuries at the present time that necessitated a player going on season-ending Injured Reserve, they could handle it cap-wise (provided that one of those two players who go on I.R. has a salary split like Brandon Jacobs or Terrell Thomas do). Another condition must be that the players who replace them have no accrues years of experience. This is why we see most in-season transactions that have to do with additions to the 53-man roster involve players with 1-3 accrues seasons of experience, especially for cap strapped teams like the Rams and Giants.
The Giants will have a healthy amount of cap room this coming off-season. This season's leftover cap room will carry over into next year's. We'll found out what that exact number is after the regular season, provided the Giants don't make the playoffs, which looks pretty likely to happen in the next week or two. Last season, the Giants carried over exactly $1,000,000 from their 2011 season "cap leftovers" into the 2012 salary cap pool.
This year's number promises to be significantly smaller than that. As mentioned above, the Giants are only $132,418 under the cap now according to the NFLPA's figures (keep in mind that the only truly 100% accurate figures are kept by the NFL Management Council, and they hardly ever are leaked). Incentives are going to factor in to the money left over at the end of the season to determine exactly how much is going to be carried over into the 2014 season's salary cap pool, so it's probable that even less than that $132,418 figure will carry over into the 2014 season's total.