My personal idea is to launch such a bloated PR campaign it plugs the hole.
Otherwise, redirect a meteoroid using nukes (that goes along with eliminating waste- getting rid of nukes), and direct it directly on top of the well, the force would be so great that it would destroy the well and the molten meteorite plus bedrock would seal a cap over the now-buried well.
Somehow I don't think that one Senator's idea of throwing beer-making ingredients in there will work though.