Note how this legislation continues to be directed at you and me. The solution to corrupt policians involves threatening *us* with fines and prison for not doing our proper bits. It's not as if our elected leaders can help it, they're practically victims! Just going on with the system they've been given by a degenerate populace. No point in cracking down on the way they behave. But eventually in spite of us they will obtain their utopian society, I suppose -- just have to keep restricting us until we get into our thick heads to behave the perfect way they have envisioned for us, and then everything will be swell.
To properly understand what Obama means by the undue influence of money, you have to unpack the political dialect a bit. Obama was ushered into his latest term on a >$1 billion campaign, and has turned his back on statements about lobbyists and public financing, so it's not that he abjures the influence of money in politics. But it is bad when money is wielded to effect by the other party. (The other party is in fact the only one capable of corruption, one's own party might have some rogue individuals who make regrettable decisions, but their political principles are, if anything, redemptive.) This statement comes on the tail of the 2014 election, in which Obama's party was routed, due largely to poor turnout. In general democrats fair better from greater voter turnout. So this would be a nice fix to that, and probably would decrease the influence of money in politics, at least in the sense that it would not longer be needed to mobilizing voters and could instead be spent in focus on telling them which way to vote.
Of course, any electoral change is going to benefit one party or the other, and they will decide their allegiance to it accordingly. But I think it's sound to say any idea that comes out of party leadership is not going to be about "reform" it is going to be about consolidating their own power. Changing election mechanics is not going to be the means of rebuffing them and kicking them out of power. It is going to be the thing to do once we've built up the spine to kick them out ourselves.