The facts–as elegantly stated in a Congressional Research Service study that came to the same conclusion–are these:
The estimated effects of the cap and other elements of the budget package depend on whether the proposals are compared with the current tax rates of 33% and 35% or the rates scheduled for 2011, 36% and 39.6%. Compared with current rules, estimated effects are between one-half a percent and 1% decline in charitable giving . . . . When compared with tax rate provisions in 2011, charitable deductions are estimated to fall by about 1.5% if only the cap is considered, but if income effects from the entire budget package are included contributions actually rise 2.5%. The relatively modest effects of the proposal arise because (1) the effect of caps on the subsidy value is limited, (2) only a fraction (about 16%) of charitable giving is affected, and (3) because evidence suggests that behavioral responses to changes in subsidies are relatively small.
(Emphasis mine.) To paraphrase: the tax subsidy isn’t much reduced; that small reduction doesn’t affect 84% of charitable giving; and, in fact, charitable giving isn’t all that tied to tax benefit.
So whether we take the IUPUI findings that charitable giving is likely to decline modestly if these tax reforms are enacted, or the CRS findings that it might actually go up, we should realize that everyone who’s hyperventilating about the impact of these changes on their poor struggling private school, museum or hospital should just take a deep breath.  Given that the reforms will support many of the social programs, environmental protections, educational institutions and health care options the nonprofits themselves seek to provide, it’s about time for the community to stop whining and agree to pony up.