I am short on time but would like to see Machu Picchu while in Equador and Peru. Is it possible to fly from Quito to Lima and then see Macchu Picchu all in one day?

Not a chance.
From Lima you have to fly to Cusco, from Cusco you have to take a train to Agua Caliente, and from there you have to take a bus.
If all those legs left in sequence - which they don't - it would be a minimum of five hours before you got to the site.
Your only option would be to take a helicopter from Cusco, and God only knows what that would run.

We've been told the helicopter does not run any more due to damage caused to MP area. We've got 3 days from Lima so will be a rush but worth doing. Lan peru flights are US116 Lima/Cusco/Lima then US89 for train from Cusco to A. Calientes return trip. We were going to give it a miss until my cousin who has lived in SA for 4 years said it is "unmissable". Can you reschedule something? It appears access to MP will be limited in the future due to too many visitors damaging the area. Try to see it if you can.

Thanks for the replies. Turns out I will have a weekend in Quito. Hopefully I can pull it off.

You'll need even more time than a weekend. You'd need to fly to Lima, then change planes for Cusco, and none of that could be accomplished before the very early morning trains leave for Machu Picchu. You'd arrive back from Machu Picchu in Cusco on the train in the evening, and, that I remember, there are no night flights to or from Cusco's airport.