Although many Conservative congregations in the 20th century eliminated the custom of reciting "tahanun," the daily supplication that is found in the Shaharit/morning service immediately following the Amidah, we recite it at Temple Israel. And I must confess that it is one of the holier moments for me in daily tefillot.
This is a prayer of entreaty, in which we quietly, almost internally, confess our failures before God, and ask for mercy. We physically imitate the posture of supplication by performing "nefilat apayim," falling on our faces, by burying our heads in the crook of our weak arm (or the other one if wearing tefillin). It is a deeply personal moment, one in which we set aside our pride, when we plead helplessness.
A dose of humility at dawn always puts a positive spin on the day.