After receiving the note, Walls re-read the jurors instructions on how they should reach a verdict and sent them home an hour early to rest before returning to court on Tuesday.
Walls encouraged the jury to put their past experiences behind them and "start fresh" with the new alternate juror.
Arroyo-Maultsby was dismissed so she could go on a pre-arranged vacation.
Evelyn Arroyo-Maultsby spoke outside the courthouse after the jury was unable to reach a verdict after three full days and part of a fourth. "Forget about what happened last week". Some of the jurors were dismissive of her opinion because they knew she would not be able to continue deliberations after Thursday, she said.
Prosecutors have accused Menendez in a bribery scheme in which he received gifts from a Florida ophthalmologist in exchange for political favors. That juror said that she felt the panel was deadlocked - and that she felt strongly that Menendez was not guilty. Walls said the comments have had no effect on the jury and told the attorneys, "She was on your side".
Arroyo-Maultsby's descriptions of last week's deliberations, if accurate, forecast problems for the prosecution.
"All of this is unique and atypical", Vartan said, but "as a prosecutor, you don't want this sort of feedback from someone who heard all of the evidence".
If the jury officially deadlocks in a mistrial or acquits Menendez of all charges this week, the senator won't be the only one breathing a sigh of relief. The Democrats have 48 seats in the Senate compared to Republicans' 52.
Should Walls formally declare a mistrial, former federal prosecutors predict that the Justice Department would ultimately refile the charges.
New Jersey Gov. Chris Christie, a Republican, leaves office on January 16, 2018.
Prosecutors in Menendez case said Melgen had offered up his private jet for the two-term senator's use, showered him with luxury trips and steered more than $750,000 in campaign contributions to entities supporting Menendez.