And the Hastert Rule?

Rand Paul proposes guaranteed immigration vote to end shutdown

Why would Ryan refuse?

Could a too immigration-friendly result come in violation of the Hastert Rule (aka the "majority of the majority rule"), named after Republican House Speaker Dennis Hastert and requiring that a Speaker of the House never allow anything to come to a vote unless it has the support of a majority of his own party?

Ryan would be unseated by the hard right of his own caucus if that happened.

“It's gamesmanship and partisanship.

I gave them the answer how you solve this today:

Promise, guarantee in writing to the Democrats that there will be one week's debate on immigration and a vote on an immigration bill some time in the next month in the House and the Senate,” Paul said on CNN’s “State of the Union.”