Congress broke a rancorous stalemate Tuesday to pass legislation designed to avert the so-called fiscal cliff. But the compromise bill, which blocked most impending tax increases and postponed spending cuts largely by raising taxes on upper-income Americans, left a host of issues unresolved and guaranteed continued budget clashes between the parties.

U.S. stocks vaulted higher on the first day of the new year, joining a global equity rally after Congress's last-minute agreement on the deficit. The Dow Jones Industrial...