As Democratic senators gathered on Tuesday for their closed-door weekly luncheon, they heard from their California colleagues, Alex Padilla and Adam Schiff, who carefully differentiated between isolated cases of vandalism in Los Angeles and the larger number of peaceful protesters who swarmed the streets to oppose President Trump’s deportation efforts.

At roughly the same time, Mr. Trump was across town in the Oval Office unspooling stories of violence, asking the assembled cameras, “Did you see the guy throwing the rocks at the police cars?”

For Democrats, the scattered yet searing scenes of unrest in Southern California have uncomfortably thrust to the center two issues that have powered Republican gains in recent years — immigration and crime — as party leaders worry that the president is setting a dangerous political trap with provocations too outrageous to ignore.

Mr. Trump’s extraordinary decision to send military troops to quell domestic protesters over the objection of local authorities, including Gov. Gavin Newsom, has unleashed an avalanche of condemnation from Democrats who argue that the president’s actions were authoritarian and unconstitutional.

In an interview, Mr. Schiff urged his party to push back on Mr. Trump without falling prey to his political framing.