Exactly why Christina Romer broke from the White House now is unknown — except we assume because things weren’t going well.
But her long-term differences have been stated. An academic economist who studied the Great Depression, she wanted an even larger stimulus. Fellow-Keynesian Paul Krugman points to a good summary in this article from last year in the New Yorker:
The most important question facing Obama that day was how large the stimulus should be. Since the election, as the economy continued to worsen, the consensus among economists kept rising. A hundred-billion-dollar stimulus had seemed prudent earlier in the year. Congress now appeared receptive to something on the order of five hundred billion. Joseph Stiglitz, the Nobel laureate, was calling for a trillion. Romer had run simulations of the effects of stimulus packages of varying sizes: six hundred billion dollars, eight hundred billion dollars, and $1.2 trillion. The best estimate for the output gap was some two trillion dollars over 2009 and 2010. Because of the multiplier effect, filling that gap didn’t require two trillion dollars of government spending, but Romer’s analysis, deeply informed by her work on the Depression, suggested that the package should probably be more than $1.2 trillion. The memo to Obama, however, detailed only two packages: a five-hundred-and-50-billion-dollar stimulus and an eight-hundred-and-90-billion-dollar stimulus. Summers did not include Romer’s $1.2-trillion projection. The memo argued that the stimulus should not be used to fill the entire output gap; rather, it was “an insurance package against catastrophic failure.” At the meeting, according to one participant, “there was no serious discussion to going above a trillion dollars.”