There are many moral reasons for more progressive taxation, but that is not really what this particular piece is about. People who fully agree with you on the moral part (including me if I were American) are probably already Democrat supporters.

The target here are people who fear that being too progressive in taxation will hurt the economy somehow, especially small businesses who are perceived as particularly important (and morally deserving) parts of the economy.

From that point of view, I don't think these people's arguments are strong. There are ways how Obama's tax plan may help or hurt the economy, but the mechanisms in this transcription are not among them. It's simply replacing Republican jabbering by Democratic jabbering.
Which I suppose is good if you suport the Obama tax plan for other reasons.

You give two new mechanisms: rich people save more and spend less of a boost in their income, and the countercyclical effect of unemployment benefits. I think the second has been well-observed, but is raising unemployment benefits in Obama's plans?

The first one is more troublesome. I mean, does America really need even lower savings rates? There might be some short term benefit from lowering taxes, but only if they are well timed as countercyclical spending. In general, changes in the tax system are not the best way for Keynesian policies.