l have a 2001 GMC Jimmy. When l tried to push button to put into 4WD, the light just blinks and wo not get into 4wd. any thoughts what this might be?

The reason the 4x4 tight is blinking is because there is a fault in the system. But u knew that already.

Before u go spending money, here is what l want u to do.
on the passenger side, remove the right lower hinge trim panel (right next to the door) behind u will find the 4x4 module.
disconnect the 2 plugs for about 30 seconds (module have tendency of locking up)
IMPORTANT. look at the plugs for signs of corrosion (very common)
if OK, then plug them back in & try to Switch to 4 hi.
If OK, no further action needed.
If not, then the system needs to be diagnosed, the module stores the failed code, & a scanner is a must.