Sorry to disagree with Peachey. "We are at the end of the day." is a complete sentence. It's just not a complete thought. That is... it leaves the listener asking "and so...?" One might expect a complete thought to include some other assertion about what the implication of being "at the end of the day" is. Examples: 1) "We are at the end of the day and so we will stop here although we have not completed our work." 2) "We are at the end of the day and I think we should congratulate ourselves for having worked hard all day." 3) "We are at the end of the day but, since our work is not done, we will have to work into the night."

"Does it exist?" Yes, but as part of a longer sentence. This phrase is not complete in itself.