As chairman of the House Ways and Means Committee, and the Budget panel before that, Rep. Paul Ryan (R., Wis.) has dealt with some of the most contentious issues not only in the House, but also within the Republican Party, where spending and the reach of government are often flash points. Here’s where he stands on some key issues.

DEBT LIMIT: Voted against legislation in October 2013 to end a partial government shutdown that also raised the debt limit. “We’re just kicking the can down the road,” he said in a statement at the...