If there was actually a push to abolish pennies, it would become a partisan/political issue immediately and all rational discourse would evaporate.
If you really want to see the penny go away, do what I do: literally throw them away. I did the math and found that the time, space, and attention needed to deal with them was costing me more than 1 cent per coin.
I estimate that I have thrown away about $10 in pennies over the last few years and don't miss a single one.