On April 21, Mr. Musk lined up $46.5 billion in financing. He had obtained commitments from Morgan Stanley and other lenders for $13 billion in debt financing, while another group of banks promised $12.5 billion in loans against his stock in Tesla. Mr. Musk added that he would use another $21 billion in cash to buy the rest of Twitter’s equity.

The financing forced Twitter’s board to take Mr. Musk seriously. No other offers for the company had emerged, two people familiar with the deliberations said.

At Twitter, Mr. Taylor weighed employee uncertainty and the societal implications of a deal versus the board’s fiduciary duty, people with knowledge of the situation said. That meant making a decision based on whether Twitter could reasonably achieve a value better than what Mr. Musk had put forward.

Mr. Taylor and other board members debated whether Twitter’s user and revenue growth prospects were realistic. The San Francisco company, which had not turned a profit for eight of the last 10 years, had set aggressive business targets.