Extend the Bush tax cuts for a short duration - 2 yrs - because the economy still wasn't clicking along well enough for the private sector to start hiring folks AND the tax cuts would allow people to "keep more of what they earned" OR provide tax credits to those who qualified. At the same time, the President got unemployment benefits extended to those people who are still looking for work.
It was a good compromise. For as the GOP leadership has continued to argue, "You don't want to raise taxes on people who are still struggling financiallly in the midst of a recession." That mentality is equally shared by members from both parties.