WASHINGTON—Lawmakers returning to Washington face a tight calendar and a dizzying list of legislative tasks, from a major tax overhaul to a new federal spending agreement, with the added complication of sexual harassment allegations that are reverberating in the halls of the Capitol.

For weeks, the political spotlight has focused on Republicans’ efforts to pass the first major revision of the tax code in more than three decades. After failing in their push to dismantle the Affordable Care Act earlier this year, GOP lawmakers...