Nancy Pelosi is all about winning. Regarded by many as her party’s most ruthless tactician, she fought her way to the top of the Democratic leadership in the House, won the majority not once but twice and retained her speakership by putting down a rebellion from younger Democrats demanding she pass the torch to a new generation.

And the former speaker is in no mood to start losing now, as evidence mounts that President Biden is staring at a major defeat that could drag his party down with him.

In private conversations with Mr. Biden, colleagues and allies, Ms. Pelosi, the Californian who still wields tremendous influence in her party and is seen by many as key to resolving the status of Mr. Biden’s candidacy, has let it be known in the days since his disastrous debate performance that she is skeptical that the president can win. And his loss, she fears, could cost her party its chance to win back the House, potentially its only firewall against a second Donald J. Trump presidency.

Ms. Pelosi, according to those who have talked with her, conveyed those sentiments in phone calls with the president and with alarmed colleagues who have reached out to her for guidance on what to do. The former speaker is intimately familiar with the minutiae of campaigns from her years following House races district by district, and she has been marshaling her knowledge of the political map, polling data and fund-raising information to press her case with Mr. Biden.

One ally said that Ms. Pelosi told Mr. Biden in a recent call that she had seen polling data suggesting that he could not win, and the president had pushed back, saying he had polls showing otherwise.

Ms. Pelosi, never shy in such situations, challenged him on that.

“Put Donilon on the phone,” Ms. Pelosi told the president, referring to Mike Donilon, the president’s longtime aide, according to people familiar with the exchange, which was reported earlier by CNN. “Show me what polls.”