But another model of congressional leadership is to try to shape his caucus rather than having it shape him. As the Emory political scientist Randall Strahan detailed in his book, “Leading Representatives,” there is a history of speakers, such as Henry Clay, Thomas Reed and Newt Gingrich, who have taken enormous risks to push their caucus in new directions.

This is a strategy that could produce historic legislation. This is the path that Speaker Tip O’Neill took, to the chagrin of many liberals, when he worked with President Reagan’s administration to pass the tax cut of 1981. Rather than standing in the way of the tax cut, O’Neill decided to sign on and demanded goodies for Democratic constituencies. House Democrats, who had little love for Reagan, had little choice but to join their speaker, knowing that they were going to lose.

With the case of immigration, Boehner could enter into a dramatic bipartisan alliance that would leave him with much greater national clout. Even the threat of an alliance might be sufficient to move enough conservative House Republicans, who sense that defeat is inevitable and decide that they might as well win some credit for the victory.

Finally, there is always the power of pork.