The demand siders assume that the problem is lack of effective demand in the economy. That businesses aren't investing because they are not confident anyone will buy their products. Furthermore, lower taxes or incentives will have little impact since firms are making huge profits and have even larger accumulations of cash which they are not investing. Furthermore, they would argue, that it is deregulation that got us here in the first place.
They would suggest restoring the confidence of consumes by quenching their desire for fairness and ensuring that the people who created the crisis are those who are paying for it. The public doesn't have any confidence in government to a large extent because they believe the government looks after the interest of big corporation and banks and does little to represent them. Perhaps, if there was an effort to create more fairness in the distribution in the costs of the recession and lay the blame where they think it belongs, then consumers may have more confidence, provide more political support for a bigger stimulus and perhaps be willing to go out and spend more. This approach incentivizes buying.
Supply siders respond by saying, nonsense, now you'll really scare them and they will never invest again and take all their money to Greece or China.
What is the answer for restoring confidence? I think a little of each perhaps. Signal to the public that you believe that the middle class and the poor have paid too much of the cost of the recession and that Wall Street and their owners need to pony up a larger share. But combine this with a thoughtful and certain long term deficit plan.