Infrastructure and middle-class tax relief are two tax items on next year’s agenda that could get enough bipartisan support to move under a divided Congress.

The issues could gain momentum because they center on working Americans—a goal for Democrats who will control the House—and align with President Donald Trump’s stated objectives—a boon for Republicans who will control the Senate.

Trump—even though Treasury Secretary Steven Mnuchin has since said other priorities will take precedence—promised an additional 10 percent tax cut for the middle class in the lead-up to the November midterm elections. The president has suggested he would be open to...