Can GPS be used in lieu of DME for instrument approaches?
Yes, the details are in FAA AC 90-108:


  7. Usage of Suitable RNAV Systems. Subject to the operating requirements in this AC,operators may use a suitable RNAV system in
  the following ways.  
  
  (1) Determine aircraft position relative to or distance from a VOR (see first note in subparagraph 7b), TACAN, NDB, compass locator
  (see second note in subparagraph 7b), DME fix; or a named fix defined
  by a VOR radial, TACAN course, NDB bearing, or compass locator bearing
  intersecting a VOR or Localizer (LOC) course


And all fixes, procedures etc. must be loaded from the GPS database, you can't enter any fixes yourself based on lat/long or whatever (section 9(c)(1)).