Republicans and Democrats alike said the clarity afforded by the new legislation would help set the parameters of the sweeping changes that many expect will seek to “broaden the base and lower the rates”: That is to say, it will end many tax exemptions and exclusions and use the increased revenue to lower what are known as marginal tax brackets. (Those define what you will pay for all net taxable income beyond certain thresholds.)

In the process, policy makers hope to give the United States a cleaner, easier-to-understand tax code. Yet some of the current exemptions are hugely popular, like the deduction for home mortgage interest or for state and local taxes. Everyone wants a simple tax code, but few people want to eliminate provisions that benefit them. That helps explain why it is so difficult to make big changes.

Mr. Ryan, in his first major policy speech after becoming speaker, talked about rewriting the tax code, which has been a personal passion throughout his years in office. “You know what the first item on that agenda is? It’s creating jobs and raising wages,” Mr. Ryan said in the speech at the Library of Congress in December. “We know what’s standing in our way. Instead of a tax code that all of us can live by, we have a tax code that none of us can understand.”

After noting that Canada has lower business tax rates, Mr. Ryan continued: “The only way to fix our tax code is to simplify, simplify, simplify. Close all those loopholes and use that money to cut tax rates for everybody. Take the seven tax rates we have now and collapse them into two or three.”

The speaker is not the only one railing against the tax code. Consider the man Mr. Ryan challenged on the ballot in 2012: Vice President Biden.

“Guys, when Reagan was president there was $600 billion in tax expenditures,” Mr. Biden said in a speech last month to House Democrats, referring to the same provisions that Mr. Ryan called “loopholes.” Whatever you call them, many are hugely popular and various interest groups will invariably fight to preserve them. For that reason, big tax overhaul plans often call for a phase-in process so that any shift is not excessively abrupt.

“There are now $1.2 trillion in tax expenditures,” Mr. Biden said. “Find me a responsible economist that can justify more than $500 billion to $600 billion of those tax expenditures having any socially redeeming value whatsoever.”