WHITE SULPHUR SPRINGS, W.Va.—House Speaker Paul Ryan, speaking at a GOP policy retreat, called for overhauling government-aid programs to be a legislative priority in 2018, though his plan is likely to face difficulties getting through the Senate and to be delayed by fights over government spending, the nation’s debt limit and immigration.

Mr. Ryan, a Wisconsin Republican, focused on tightening workforce requirements for welfare and food-stamp programs in his presentation Wednesday to GOP lawmakers and “getting people the...