This would not necessarily be considered "liberal" in Switzerland, as the Liberal and FDP parties (now merged) are not liberal in the sense that Americans misuse the term.
I'm Canadian, so there's that. The Swiss are pragmatic conservatives, so this might pass if you can convince the bulk of them it makes sense financially, i.e. it will reduce overall costs of aid and social assistance programmes.
Polls, as well as the results of similar initiatives (eg minimum wages). Would need a massive shift to see it pass imo (especially since the small rural cantons have a disproportionate weight and they don't tend to vote in favor of those issues).
The Swiss have referendums all the time and most, especially liberal ones like this, fail.