With President Barack Obama’s approval ratings near a new low this week, the Democratic water-cooler talk is focusing especially early on hopes for 2016 — with the bulk of today’s attention on news that all 16 of the Senate’s Democratic women have written to Hillary Rodham Clinton, urging her to run.

The unanimity of the group means as many as three potential aspirants for the nomination would defer to the former secretary of State, adding to the sense of inevitability about her candidacy and to the expectation that her bid would essentially clear the Democratic field.

Elizabeth Warren of Massachusetts has been widely touted on the left as a worthy liberal alternative to Clinton, and she hasn’t explicitly ruled out such a candidacy. But the freshman senator’s signing of the letter appears to amount to such a demurral. Kirsten Gillibrand of New York and Amy Klobuchar of Minnesota have both publicly described themselves as Clinton supporters and have signaled they would shelve their White House aspirations if she ran next time. Their signatures lock those promises in place.

Another newsworthy signature comes from the dean of the female senators, Barbara A. Mikulski of Maryland, because it means she’s not waiting for her state’s governor, Martin O’Malley, to formalize his presidential intentions before declaring her preference for someone else.

The letter was orchestrated by Barbara Boxer of California in early spring, only months after Obama’s second term began and Clinton left her Cabinet seat. It came just as the Ready for Hillary super PAC was being created by aides to her 2008 campaign in an effort to centralize the recruiting efforts. Clinton herself has said she won’t announce her intentions before next year.

The missive was intended to be a private message to the onetime New York senator from her former colleagues, and its text has not been disclosed. Its existence was revealed Monday by one of the signers, Kay Hagan of North Carolina. “All of the Senate Democratic women have written her a letter encouraging her to run,” she told a gathering of donors to EMILY’s List, part of a series of meetings the group is staging across the country to promote interest in a female Democratic candidate.

Two other prominent Democrats committed this week to supporting a Clinton candidacy: Rahm Emanuel, who left a power-player career in the House to become Obama’s first chief of staff and is now mayor of Chicago; and Lt. Gov. Gavin Newsom of California.

The boomlet of interest in 2016 comes as a series of recent surveys shows Obama’s average job approval rating once again slipping below 44 percent. It’s generally been above that benchmark since the summer, but it’s been dragged down by a welter of problems — spying by the National Security Agency, the balky approach toward Syria’s chemical weapons, the government shutdown and now the multifaceted troubles for the rollout of his health care law.