With no other powerful Democrats likely to run against her, Hillary Rodham Clinton’s toughest adversary for her party’s presidential nomination in 2016 has now become clear. It is an opponent that challenged her in the early 1980s over her use of her maiden name — and was hectoring her again on Tuesday over her use of personal email for State Department business.

“Did you or any of your aides delete any government-related emails from your personal account?”

“What lengths are you willing to go to prove that you didn’t?”

“The White House Counsel’s Office says that you never approved this arrangement through them. Why did you not do that?”

Probing, persistent questions like these from the political press corps at Tuesday’s news conference are the sort that rival candidates would be expected to ask on the campaign trail or in televised debates, as Barack Obama did against Mrs. Clinton in 2007 and 2008 over the Iraq war and other issues.