They tested data from the General Social Survey and two other sources to explore a number of different hypotheses. Was it a reaction against growth in government under Obama — the so-called "government overreach" hypothesis? Lingering racial animus affecting views of a government now headed for the first time by an African-American? The product of a war of ideas in American political life that was shaping public opinion independently of macro-economic circumstances? And what was the role of "motivated reasoning" — the all-too-common intellectual habit of insisting on a belief in the face of contrary evidence, and especially in times of stress?
They systematically tested hypotheses until they were left with one conclusion: The Great Recession caused everyone to double down on what they already believed about the proper role of the individual and the state, with Republican sentiments intensifying more sharply against new government programs than Democratic ones changed in favor. “For several decades now, the Democratic and Republican parties have become more and more distinct when it comes to the laws and policies that U.S. senators, representatives, and presidents support,” said Brooks in a statement. “This polarization is also asymmetric: Republican politicians have moved much faster to the right than Democratic politicians have moved to the left. "

"[W]hy did the U.S. public turn to comparatively lower preferences for government action during the recession?" the study authors ask in their journal aritcle. The "results point overwhelmingly to partisanship .... had only changes in the preferences of partisan identifiers occurred, there would have been a larger drop in overall government policy preferences. The public would have moved even faster away from government support during the critical 2008 to 2010 period."
That's worth repeating: The ideological shift among Republicans was so intense that support for government programs would have been even lower during the 2008-2010 period if not for the recession, which somewhat mitigated the decline.

Racism dropped slightly between 2008 and 2010, the authors found, and if it were the major factor in shaping public opinion about government programs, there would have been movement in support of programs instead of against them. "Trends in racialized reactions among voters — first to Barack Obama’s candidacy and then his presidency — are unlikely by themselves to have constrained public willingness to consider new federal programs and a larger role for government," the authors conclude.
Instead, what they found was this:
Partisan groups responded quite differently in their policy preference formation at specific points in time, and partisan divergence was most extensive from 2006 to 2010. During this time, strong Democrats moved toward greater support for government responsibility (primarily between 2006 and 2008), and Independents trended toward lower levels of sup- port. Strong Republicans, for their part, moved even more quickly in the direction of preferring less government responsibility during the recession.
... by 2010 partisan differences in government responsibility attitudes reached an all-time high. Figure 3’s estimates identify 1994 and 2002 as earlier periods of partisan divergence, yet the recession era elicited particularly divergent policy attitudes among partisan groups.
Brooks and Manza also looked specifically at "such recession-era legislative changes as the 2009 stimulus bill or health care reform in 2010."