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"So telling truth may seem simple - just go ahead and do it - but he has the other testimony to worry about," Jeannette-Meyers said Monday on CBS This Morning.
Mr. Clinton's lawyers are probably working with him to see that both statements - the one he made under oath in January and the testimony he makes Monday - are in agreement.
In his testimony Monday, the president will have what no other American citizen has: his attorneys will be present while he answers the grand jury and the prosecutor's questions.
"It was a huge concession," Jeannette-Meyers said, "because part of the intimidation of a grand jury - and part of its power - is that you have to walk in there alone, sit up there. You have no help. If you want to talk to your lawyer, you've got to go into the hall.
"He will have three attorneys sitting with him, and they can openly object, and that will keep the president safe from going down a line of questioning that could become very dangerous."
In a January deposition for the Paula Jones sexual harassment suit that was pending against him, Mr. Clinton denied having a sexual relationship with former intern Monica Lewinsky. Although the Jones suit was dismissed by a federal judge, the president's deposition is a key piece of special prosecutors Kenneth Starr's case.
Mr. Clinton fought in the courts to keep the Jones suit from going forward while he was in office, but the Supreme Court ruled that it should proceed.
"It is interesting their theory was, it won't be much of a disturbance to the presidency, so the suit can go forward," Jeannette-Meyers said. "I think that has proved not to be the case."