I honestly can't think of any reason why Obama and Congressional Democrats should try to extend the EGTRRA and JGTRRA (i.e. the "Bush tax cuts").
The Democrats are afraid of being branded as "tax-raisers"... but that's already been happening for the past 2 years (despite the fact that they have reduced taxes) and won't change if the Bush tax cuts are extended.
The Democrats are afraid of paying a political price if they let them expire, and perhaps doing badly in an election... but that's already happened.
The Democrats (some of them, at least) may be afraid that the rise in tax rates in January will hurt the economy... but as Menzie points out, the impact on the economy is actually likely to be quite small. Furthermore, it seems highly probable that, if the Bush tax cuts expire, there will be a serious push early in 2011 to cut taxes, resulting in the negative fiscal shock to the economy being very small and very temporary (and even reversible, if you do things right).
What's more, if it comes to a brand new tax cut package in 2011, then the Democrats can have significant impact in shaping the nature and design of those tax cuts (unlike the Bush tax cuts, which they had almost no role in shaping)... AND the tax cut would clearly and unambiguously be marketable as "the Obama tax cuts".
Remind me again why the Democrats should try to extend the Bush tax cuts?