House Speaker John Boehner (R-Ohio) said Thursday that any immigration legislation will have to have the support of a majority of House Republicans in order to come to a vote.

Boehner has suggested as much before, saying last week that he had "no intention" of violating the so-called "Hastert Rule" -- which requires a majority of the majority party to support a bill before it comes to a vote. But that statement ("no intention") appeared to give him a little wiggle room.

His statement at a news conference Thursday left no leeway at all.

He said the Hastert Rule would also apply to any legislation that results from a conference committee between the House and Senate -- the likely result of the House's plan to pass its own immigration bill, rather than the Senate's version.

"For any legislation, including a conference report, to pass the House, It’s going to have to be a bill that has the support of the majority of our members," Boehner said.

Boehner also echoed past statements that the Senate bill will not come to a vote in the House. The bill is set to pass in the Senate with about two-thirds of the chamber supporting it.

But even as two-thirds of the Senate is on-board, only about one-third of Senate Republicans are set to vote for it. If a similar portion of the House GOP conference supported an immigration bill, it wouldn't come to a vote under the Hastert Rule.

Boehner -- as with other speakers in the past -- has occasionally violated the Hastert Rule, and at one point even declared that it's not actually a rule (which is technically true). But conservatives have registered their dismay with him doing so, and breaking it on such a high-profile piece of legislation as immigration reform would surely lead to a backlash within the House GOP conference.

The speaker's decision effectively means that in order to pass, any immigration legislation would need the support of a majority of House Republicans, a majority of the House overall, and likely at least 60 senators.