With the Citizens United decision, that's no longer possible without either a Constitutional Amendment or the Supreme Court overturning their own decision - neither one is very likely.
Citizens United has implications for campaign finance, but the demise of publicly financed campaigns that GP is referring to began before that.
In fact, it began with Obama's first election (2008), in which McCain agreed to take public financing. Obama, on the other hand, broke his earlier promise to take public funds, becoming the first candidate in history to do so[0][1]. Because accepting public financing means limiting total spending, Obama vastly outspent McCain by November. Obama won the popular vote, spending $10.94/vote, whereas McCain spent only half as much total money (amounting to $5.97/vote in the end.)[2]
[0] http://www.nytimes.com/2008/06/20/us/politics/20obamacnd.htm...
[1] http://www.nytimes.com/2008/06/20/us/politics/20obama.html
[2] https://en.wikipedia.org/wiki/Fundraising_for_the_2008_Unite...
So even a bad SCOTUS decision could stay on the books for a long time - just to save face and uphold the credibility of the institution.
They look to rock the boat the least. Even in their current hyperpartisan state.