On paper, the Republicans still have a big geographic advantage: There are only nine Republican-held districts tha t voted more favorably for Democrats in the last two presidential elections than the rest of the country did. But that advantage doesn’t seem to be helping the Republicans as much as it has in past cycles, when congressional election results were increasingly correlated with presidential results.

Instead, Democrats appear highly competitive in many conservative districts. Already, there are polls showing Democrats ahead in Kentucky’s Sixth District, West Virginia’s Third, North Carolina’s Ninth, New York’s 22nd and Montana’s at-large district. Mr. Trump won each by at least 10 points.

One possibility is that Democrats are unexpectedly putting conservative districts into play because the overall national political environment is more favorable to Democrats than the generic ballot polls imply. Another possibility is that a district’s presidential vote choice will play a smaller than expected role in determining how a district will vote for the House.

Indeed, there aren’t many polls showing Democrats excelling in the well-educated districts where Mrs. Clinton won. Polls sponsored by Democratic groups have shown Republicans leading in Illinois’s Sixth, Pennsylvania’s First, Washington’s Eighth and California’s 39th. Even in the well-educated districts where Democrats lead in recent polls, like Virginia’s 10th or California’s 48th and 49th, the polls show Democrats merely running even with Mrs. Clinton.

Individual House polls are never much better than a rough indicator, and this is an early stage of the race. But the overall pattern is fairly clear, and a similar pattern shows up in the special election results of the last year. Democrats have run far ahead of Mrs. Clinton in white working-class areas that backed the president by a wide margin, including Conor Lamb’s victory in Pennsylvania’s 18th District in March. They haven’t run so far ahead of Mrs. Clinton in the areas where she excelled, like Georgia’s Sixth or Northern Virginia.

Recruitment could be part of the reason. The Democrats succeeded in luring many of their longtime top recruiting targets into the race in a lot of white working-class districts. They haven’t typically done a great job finding top-tier candidates in districts that supported Mrs. Clinton, in part because there are fewer elected Democratic officials to recruit in the traditionally Republican areas where she often excelled.

All of this could change by November, but as we n ear the start of the general election season, t he initial battleground map extends well beyond the districts she won in 2016.