MOBILE, Ala. — Senator Doug Jones of Alabama waved a stack of legal pads in the air — all of them filled with his notes from the opening days of President Trump’s impeachment trial — and insisted he needed to hear more facts. “Yesterday’s evidence was pretty compelling,” he said in a video posted to his Twitter feed last week. “So I’m anxious to see what the president will say and do.”

Mr. Jones has recorded five-minute segments like these every morning since the trial began to try to answer why he is still undecided on a question that most Americans resolved long ago. “I caution everyone that we’re still in the early stages,” Mr. Jones, a former trial lawyer, said in another video. “We’ve got to hear the other side of the story.”

As the lone Democrat in the Senate representing the Deep South, a region that is solidly pro-Trump, Mr. Jones is in a precarious position. Political prudence demands that he take an exceedingly measured approach to his vote on whether to remove Mr. Trump from office. The senator has spent weeks pleading for open-mindedness, even going so far as to raise doubts about the Democrats’ case against the president, saying last month that “there are gaps.”

The challenge for Mr. Jones is whether voters see him as reasonable and unbiased, as he hopes, or as an appeaser of the other side. His appeals risk alienating not only the Trump-supporting Alabamians he has to answer to when he faces re-election in November, but also liberal Democrats — his base — some of whom he says have wanted to remove the president since “the minute he took his hand off the Bible when he was sworn in.”