You're asking the wrong question. If the Senate Democrats really opposed the debt limit bill, why didn't they use their superminority to block it via filibuster?
Answer? Posturing.
They knew even then that voters didn't really understand the debt ceiling (in fairness, it doesn't make a hell of a lot of sense, anyway). They could oppose it, score cheap political points, and still be completely assured that the bill would pass.
Simply put, they took advantage of their minority status to avoid doing something hard. We've seen that the GOP is also good at this game. The problem, as I mentioned a few posts ago, is that the House GOP has been slow to recognize that they are now the governing party.
eta:
Eric Cantor is failing. It's not his job to tell Boehner and Obama that the votes aren't there in the House. It's his job to make the votes there. That's the entire reason for his position (along with the Whips). To do the hard work of rounding up tough votes. Cantor is not doing what's best for his country, or even what's best for his party. Cantor is riding the TP wave and doing what's best for Cantor.