Elizabeth Warren and Hillary Clinton testifying during John Kerry's confirmation hearing in the U.S. Senate on Jan. 23, 2013. Reuters

Thousands of Americans across the country are gathering at events this weekend to urge Democratic Sen. Elizabeth Warren to run for the White House in 2016. Supporters from several political organizations are hosting hundreds of events in 46 states plus Washington, D.C., Puerto Rico and Guam to help draft the Massachusetts senator into the presidential race, according to a press release from Political Action, a federal political action committee.

Warren has said she will not run for president, but that hasn't stopped the chatter around a potential 2016 campaign. Warren became the first female senator from Massachusetts in November 2012 and joined the Senate Democratic leadership team last year. The former Harvard Law School professor has advocated for student loan reform and Wall Street regulations.

If Warren launched a 2016 presidential campaign for the Democratic nomination, she would likely face former Secretary of State Hillary Clinton, who has all but announced a run and is the presumed front-runner. Although the two female politicians are cut from the same Democratic cloth, Warren has disagreed with Clinton on a number of issues. The anti-Wall Street proponent slammed Clinton in her 2003 book for switching her position and voting for a bankruptcy bill in 2001 that makes it more difficult for credit card holders to renegotiate debt.

"As first lady, Mrs. Clinton had been persuaded that the bill was bad for families, and she was willing to fight for her beliefs,” Warren wrote. “As New York’s newest senator, however, it seems that Hillary Clinton could not afford such a principled position. ... The bill was essentially the same, but Hillary Rodham Clinton was not.”

Many left-wing Democrats have encouraged Warren to challenge Clinton in a 2016 run for the White House. Nearly 300,000 Americans have signed up in just over a month to support the "Run Warren Run" campaign, which is backed by Political Action, Democracy for America and Ready for Warren, according to the press release.

The organizations cited Warren's leadership style and advocacy for working and middle-class families as driving forces behind the movement. Those who attend one of the 224 organizing house parties on Saturday and Sunday are expected to discuss ideas on how to convince Warren to enter the presidential race, according to the press release.