Page 5 will show you the parts break down for the Juicy 7 brakes.  The two parts I am describing would be 21 (Push Rod) and the left most part of 13 (Worm Gear Kit).

NOTE: Be sure brake is bled properly before making this diagnoses.  If the brake is not bled correctly, the lever could exhibit this same kind of feeling.

To the right you will see parts I am describing.  The top one is what it looks like assembled. The bottom one shows the parts separated.
Click on picture to get a larger view. Detailed picture of the push rod and the cup mechanism.	Click on picture to get a larger view. Detailed picture of my "bad" unit.  If you look closely, there is deformation of the  plastic piece.  The ball end of the push rod should be clipped in snug with out any free play.  If you pull lightly on the end of the rod, it should not move.  If  it does move,  this will attribute itself to the free play experienced at the lever.
Picture of the Worm Drive Rebuild Kit SRAM Part # 11-5309-762-000 About $25 US from bike shops.	Click on picture to get a larger view.

Tools: Needle Nose Pliers Small Screw Driver 2.5 mm Allen Wrench 2 mm Allen Wrench

Initial Set up and Pivot Pin Removal: I removed the brake from my bike and worked on a bench.  This was easier (to me).  If you choose not to remove the brake from the bike,  it should be okay, just be careful not to spill fluid when you take the lever apart. Also, I put the red plastic piece between the pads.  Do this to insure you do not push the pads out while doing this work.  Start by removing the pivot pin. Using the 2.5 mm allen wrench, back out the Set Screw just enough to allow the pin to drop out.	Click on picture to get a larger view. Removal of Pivot set screw Click on picture to get a larger view. Removal of Pivot Pin
Pin out - Removal of C clip and Star Wheel: First picture shows pivot pin now removed.  Set pin aside and use a small screwdriver to remove the C Clip.  Be careful it doesn't go flying off into oblivion. Remove the Star Wheel by un-screwing (Lefty Loosey) the unit out.	Click on picture to get a larger view.     Pin Removed Remove C Clip Unscrew Star Wheel
Removal of Lever (Seperation of lever from lever assembly): Using the 2mm Allen Wrench Screw in the reach adjust screw. Keep turning until the lever is separated from the lever assembly. Set the Lever aside.	Click on picture to get a larger view. Screw in Reach Adjust Click on picture to get a larger view. Lever assembly minus the lever.
Remove the Worm Drive Assembly: Using the 2mm Allen Wrench Remove the Worm Drive Assembly by unscrewing the unit from the lever assembly.  This uncsrews the unit from the Master Cylinder.   Be very careful to have the lever in the up position so the fluid doesn't come spilling out of the lever.	Click on picture to get a larger view. Unscrew reach adjust to back out Worm Drive Assembly. Click on picture to get a larger view. Worm Drive Assembly removed. If you look closely, you can see the Master Cylinder (White part). Try to hold the lever in this position so the brake fluid does not drip out.
Assembly (mostly reverse of disassembly): After you remove the old unit. Set the old unit aside. Screw in the new Worm Drive Assembly (2 mm AllenWrench) Screw in and clip in the Star Nut (Needle nose pliers)  Be careful not to loose the C Clip Screw the lever on to the lever assembly via the reach adjustment screw.  (2mm Allen Wrench) Insert lever pivot pin Set pin in place using set screw and 2.5 mm Allen Wrench. Mount brake on bike.  You may have to bleed the brake.  I didn't have to.  Good luck.