Yet just as the would-be leaders of the committee, who were assembled for the first of four officially sanctioned candidate forums, preached prudence and calculation in the Trump era, others in the party were responding with fury to the president-elect’s latest Twitter outburst.

Mr. Trump’s ridicule of Representative John Lewis of Georgia as being “all talk” set off outrage among Democrats, with many defending their colleague, some vowing to join him in boycotting the presidential inauguration, and most determined to make Mr. Trump pay a price for taking on a giant of the civil rights movement. Mr. Lewis had said a day before that Mr. Trump was not a “legitimate president.”

The president-elect’s willingness to attack seemingly any and all comers — Mr. Lewis is one of the few figures revered across party lines — nearly every day makes him an even more difficult target for Democrats.

Less than a week before Mr. Trump is sworn in, there is a widening disconnect among Democrats over how to challenge a leader whose talent for stirring controversy can blur, rather than sharpen, the lines of attack against him.

Democrats, here and in Washington, say it is folly to engage him on his preferred terrain of insults and bombast. They suggest that one of Hillary Clinton’s mistakes was to try to isolate him from the Republican Party by portraying him as an aberrant figure.