Didn't Huckabee do this in Arkansas?
He set up a special fund for the state to do social programs and set up voluntary contributions to it.
After a couple years it had $1200 in it and $1000 was from a rich leftist. It was done to prove that if given the choice, people will not pay taxes.
On the other hand, voluntarism already exists in America. My church, which is fairly small and operates on a comparatively shoestring budget, in addition to being a place that does fairly unaccounted direct work within the community like dinners and education programs, still manages to send several tens of thousands of dollars out of the county every year for charitable purposes elsewhere.
Get rid of the IRS, and that shoestring budget gets a lot bigger. Remember where all the tsunami relief money came from? Philanthropists. Remember who went to the gulf in droves when FEMA screwed up? Philanthropists. Believe me, the poor will be taken care of without the programs.
So whatever gets signed, it's gotta say that.
The other thing I'd add, is that you have to realize that to lawmakers other than RP, and to the vast majority of America, this little world we've carved ourselves here doesn't exist. I'm not sure what effect a petition would have, unless it had 100 million signatures on it.