A few of the senators have discussed with Warren the possibility of publicly backing Clinton. However, they’ve been careful not to put a lot of public pressure on their colleague, who is fiercely independent and has a loyal following among progressives.

“I’m hopeful she’ll join us. I’m hopeful she’ll join the revolution that will allow us to come together to elect” the first female president, said Sen. Debbie Stabenow (D-Mich.), one of Clinton’s staunchest supporters.

Asked if she or other senators had approached Warren personally, Stabenow said, “We all talk about it,” but declined to reveal what Warren has said in response.

Sen. Barbara Mikulski (Md.), the dean of the Senate’s Democratic women, has also talked to Warren about backing Clinton.

“I’ve told Sen. Warren that we would welcome her anytime she’s ready,” she said.