House Speaker John Boehner (R-Ohio). Photo by Alex Wong/Getty Images House Speaker John Boehner (R-Ohio)  (Alex Wong/Getty Images)

If immigration reform is to pass through the House, House Speaker John Boehner (R-Ohio) may very well have to break the Hastert Rule.

But before the bill can even pass through the Senate, top conservative groups are putting pressure on Boehner to stick to the rule, which prevents legislation from coming to a vote unless a majority of the majority party (Republicans in the House) support it.

And now a smattering of top conservative leaders signed their names Tuesday to a letter urging the House GOP to amend party rules to codify the Hastert Rule, in the name of promoting conservatism.

"To that end, we encourage you to formally pass the Hastert Rule that requires a 'majority of the majority' to pass legislation," the conservative leaders said. " A growing number of House members support an effort to change Republican Conference rules to codify the Hastert Rule."

The letter is signed by former Reagan attorney general Edwin Meese, Club for Growth President Chris Chocola, American Conservative Union President Al Cardenas, Family Research Council President Tony Perkins, Tea Party Express President Amy Kremer and American Values President Gary Bauer.

Boehner has broken the Hastert Rule a number of times in recent years — as have other speakers, up to and including Hastert — and emphasized a couple months back that the rule isn't technically a rule at all, but rather a guiding principle.

His office said Tuesday that the rule remains the goal.

“Speaker Boehner has been clear: our goal is always to pass legislation with a strong Republican majority," Boehner spokesman Michael Steel said.