A series of serious allegations against GOP congressmen in key House districts have rattled party insiders this week, fueling Republicans’ anxiety that they could lose seats once considered mostly safe and further endanger their majority.

The political situation is becoming dicey for Republicans clinging to a narrow House majority, underscoring how fine a line they might need to walk in the weeks to come.

A series of serious allegations against GOP congressmen in key House districts have rattled party insiders this week, fueling Republicans’ anxiety that they could lose seats once…