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Mr. Clinton on Wednesday also said he was “honored” to work with both former Bush presidents in relief efforts for victims of the 2004 South Asian tsunami, 2005’s Hurricane Katrina and the 2010 earthquake in Haiti.

But Mr. Obama himself must tread carefully when commenting about his immediate predecessor for fear of being perceived as shirking his presidential responsibilities.

“Three-and-a-half years in, you don’t want to run for re-election saying, ‘Re-elect me, the problem is his,’ ” Mr. Ornstein said.