David Corn wrote a brilliant article detailing how, in 2012, the president managed to trick the Republicans into supporting a second stimulus -- simply by allowing the renewal of the Bush tax cuts.
The package would extend the Bush tax cuts for all taxpayers for two years and would reduce estate taxes for the wealthy (a move many Democrats couldn't stand), but it also included a payroll tax cut, a child tax credit, additional unemployment insurance, renewable energy grants, and other stimulative measures. A White House chart noted that Obama had won $238 billion of stimulus in return for yielding on $114 billion in high-income tax cuts.
In a way, Obama had sacrificed a stand of principle to push a second stimulus through Congress and provide a much-needed boost to the economy.
Everyone who said the president "caved" on the Bush tax cuts owes the president an apology. By the way, here's what I wrote for The Huffington Post when the deal was announced in December, 2012.