“If I had to vote today, I would cast a ‘no’ vote,” said Rep. Emanuel Cleaver, a Missouri Democrat, who cites misgivings over the Iraq war as one of many reasons for his opposition. Mr. Cleaver is a prominent member of the Congressional Black Caucus, many of whose members signed a letter last week urging the president to seek authorization from lawmakers.

In Seattle, Democratic Rep. Jim McDermott says his office has been swamped by constituent calls opposing a Syria strike. He said he is likely to vote “no.” “I am not voting my party. I am not voting my president. I am voting my country,” he said.

Mr. Obama rose to the White House partly on the strength of his opposition to the Iraq war, and antiwar sentiment—to his peril now— remains potent within a wide swath of his party. Many Democratic lawmakers cite the lead-up to the Iraq war to explain their wariness or outright opposition to any military action now.

The Progressive Change Campaign Committee, a liberal political-action committee, said Wednesday that a poll of about 55,000 of its almost one million members found 73% oppose action in Syria. It sent a memo to all Democrats in Congress under the heading “Your base opposes military action in Syria” and launched a phone campaign to pressure lawmakers to vote “no.”