WASHINGTON—Democrats will aim to reverse tax cuts for high-income households when they take the House majority, setting up a clash with Republicans that will color fiscal debates over the next two years, including prospects for a bipartisan deal to improve the nation’s infrastructure.

Both sides have signaled they want a spending program to improve the nation’s roads, bridges, tunnels and other public works, but disagree on how to fund it. Last year, Senate Democrats proposed a $1 trillion infrastructure plan, financed largely...