NASA has some of highest approval ratings of any federal agency. However, fighting for bigger slice of the federal budget is always a difficult battle.
Why not open up specific NASA missions to supplemental funding via a Kickstarter-style website? Let us, the people that want to send a mission to Europa, help fund it directly. Let me post it to my Facebook that I've helped make a new mission possible. If I give $25, send me a bumper sticker. If I give $100, send me a t-shirt. For $1000, let me come visit my probe before launch.
NASA always wants to keep the public as engaged and excited as possible. What better way to gauge the people's interests than giving them a direct say in which missions go-ahead? Let's put a man on Mars. Give us a way to help.