"It's been a very long time since someone with modest means was elected to a national office (Harry Truman comes to mind and Ike may not have been what we would now call wealthy either). But the biggest advantage is not personal wealth but connections (people who owe you and can deliver campaign money) although Obama and his Internet grass roots supporters are changing that paradigm somewhat."
National office, perhaps - but Congress people are elected from local districts. As you say, it's not primarily money, but connections. To get connections, money helps - that's always been true, but connections are the number one factor. A lot of local San Francisco politicians were originally of modest means, and started out working in local populist or progressive movements, worked on others' campaigns, and subsequently ran on their own once they had gained enough connections...including the people who raise the money for them.
The argument for congressional pay raises always centers on the supposed "sacrifice" people make when they enter Congress - putting their regular more lucrative career aside for the public good, or so the myth goes. But the fact is that the majority of congress people make more money from their congressional salary than they did in the private sector. Once they leave Congress, they can use the connections they've gained on Capitol Hill to get more lucrative jobs than they could get before their stint in Congress.
Bill Clinton was a man of modest means - he grew up poor. Being Governor of Arkansas paid about $35,000 a year back in the 80s - Hillary grew up middle class, but was a top notch lawyer, and made most of the money in the Clinton family. But Bill and Hill were never truly wealthy until Bill cashed in on being the former President - from book sales, lecture fees, and so forth.