Dr. Adam Hamawy, a New Jersey Democrat with big-name support on the left, has touted his humanitarian work, but some opponents want to talk about Sheikh Omar Abdel Rahman.
Prosecutors would face substantial hurdles in potentially pursuing charges against Ms. Carroll, who twice won cases against Donald Trump, or the billionaire who helped pay her lawyers.
U.S. and Iranian officials say they are closing in on the terms of a preliminary agreement. Yet sticking points, particularly over the Strait of Hormuz, remain.
The Justice Department is said to be examining the funding of lawsuits brought by E. Jean Carroll, an author who has never sought a public role, political power or governmental authority.