Both pilots attempting to enter a crossing restriction into the FMC of their B737NG resulted in a failure to install the cleared altitude into the altitude alert window. Flight crew's failure to meet a crossing restriction resulted.

Narrative

Inbound to PHX on the EAGUL Arrival at FL 380; ATC issued; 'Cross 15 miles east of SLIDR at 360.' Some confusion ensued as the First Officer and I discussed how best to set up the FMC to cope with the clearance; and as I was doing the math and trying to enter the point 3 miles east of DOJOE. My First Officer; in trying to be proactive; simultaneously was trying to delete DOJOE and create a new waypoint. We then cooperated our efforts and got the restriction correctly entered in the FMC; but during the confusion neglected to set 360 in the altitude window. Late recognition and diagnosis of why the airplane did not descend at the appropriate point led to missing the crossing restriction. When given a crossing restriction that is just 2000 FT below cruise altitude; there is very little time to correct a late descent. Automated descents must be carefully monitored to insure correct response. More focused attention just prior to top of descent would be key to timely corrections. An immediate descent would have also prevented the error at a negligible fuel cost.