I doubt it. And Backer's examples certainly don't convince me.
The National Rifle Association spent nearly $20 million in the 2012 election on outside spending, making it the 15th largest independent spender. Is it any wonder senators facing tough re-election contests in 2014, such as Mark Begich (D-Alaska), Mark Pryor (D-Ark.), and Lindsey Graham (R-S.C.), voted against universal background checks for gun purchases despite near-consensus support among the public?C'mon. Does anyone, really, believe that it's campaign finance, rather than fear (justified or not) of voters' reaction to the policy position, which drove the votes of these Senators? Yes, yes, background checks polls really well -- but gun control doesn't in the states of those Senators who voted against it. Those Senators are almost certainly driven by the campaign messages that would be used if they voted the other way, not the incremental change in how much campaign money they and their opponents would have. Surely it's not as if gun control used to pass easily before Citizens United opened the floodgates.
Second example? Even weaker:
And while the threat of a double-dip recession couldn’t persuade Congress to avert the self-imposed sequester, the typically languid House and Senate did manage in a mere six days to grant the Federal Aviation Administration more flexibility in managing the cuts — the only exception of its kind. While 800,000 workers experience cuts to unemployment benefits and 140,000 fewer families receive low-income housing vouchers, those people don’t exert enough power and influence to extract concessions from Congress. Would these people have more clout if they had the means to make large campaign contributions?Where to begin...well, first of all, there is no Super PAC for air travelers. So the assertion that it's campaign finance that makes elected officials especially responsive to them appears to be an enormous stretch. Why might politicians care more about airport delays than low-income housing? Well, first of all, a lot more people fly than receive government housing assistance. Second, the middle class and wealthy people who fly are more likely to vote than poor people are. Third: politicians themselves spend tons of time in airports, but no Member of Congress qualifies for low-income housing help. Fourth: Members of Congress, successful professionals all, tend to have social networks largely composed of those middle-class and wealthy people crowding the airports.
Would any of that change if campaigns were financed differently? Nope. It's worth recalling that the two presidents elected during the era of almost pure (general election) public financing, Jimmy Carter and Ronald Reagan, were no different than presidents elected before or after them on these sorts of issues.
Stepping back from these particular examples...the main effect, in my view, of the hunt for campaign money is that on the time of the candidates; we've read the horror stories of how much time Members of Congress are expected to spend raising money, and that is a real scandal. My reading of the research (and I'll admit I'm not fully up to date), however, is that it's very difficult to connect campaign donations to particular acts that legislators make. That's especially true for high-profile issues such as guns. If campaign donations change policy positions of politicians, it's most likely to happen on obscure, little-reported (but still perhaps important) measures, especially ones that no one in their district has direct interest in.
As it happens, I'm in favor of partial public financing of House and Senate elections (floors, not ceilings!). But not because I think that it would magically change the interests represented in Congress.* The truth is that there are lots and lots of reasons why politicians pay more attention to wealthy and middle class constituents than to poor ones, and it's not clear that campaign finance is on the list of reasons at all, let alone at the top.
*Why then? In order to encourage at least minimally competitive elections in far more seats. Far too many House and even Senate elections fail to attract quality candidates from both major parties; I think partial public financing would stand a very good chance of improving that situation.