A restive group of newcomers. Baffled party leaders. Fiery conversations behind closed doors that spill into public view and threaten to upend legislation. After a wrenching week for Democrats, it’s hard not to wonder: Does Speaker Nancy Pelosi have a tea party problem? Emboldened by their ability to seize the spotlight and shape the national debate, a core group of high-profile freshmen Democrats are driving an agenda that could define the party for years to come. Much like the tea party conservatives who vaulted Republicans to power a decade ago, these Democrats’ firm ideology and wait-for-no-one swagger have set off...