File: Sen. Ted Cruz (R-Texas) (AP Photo/Senate TV)

Sen. Ted Cruz (R-Texas), a favorite of tea party activists, met with more than a dozen House Republicans for breakfast Wednesday morning and urged them to ratchet up their pressure on Democrats on measures to stem the current influx of migrant children at the southern border.

According to several attendees, Cruz told the group to hold firm and not buckle to demands from the White House or Senate Democrats, should they ask House Republicans to compromise on the scope and cost of legislation.

The closed door meeting came an hour before House GOP leaders unveiled their own plan to address the migration crisis and underscores the growing divisions in the Republican Party over how best to move forward, with Texas Rep. Kay Granger's task force and House Speaker John Boehner (R-Ohio) seeking consensus on their proposal while Cruz and movement leaders separately advise House conservatives on their strategy.

Cruz spoke at the gathering, a meeting of the Conservative Opportunity Society, at the invitation of the group's chairman, Rep. Steve King (R-Iowa), a prominent critic of bipartisan efforts to pass comprehensive immigration reform.

"He's a perfect catalyst and he has a real rapport with conservatives in the House," King said in an interview later Wednesday morning. "He really wanted to hear from people in the room. He also let us know that anything we send to the Senate, if it comes back, it's going to be terrible, so we should make sure we're ready to respond to that."

Rep. Matt Salmon (R-Ariz), a member of the Granger-led working group on immigration, was one of the attendees at the meeting and shared his group's framework with the freshman Texas senator. But King said that he and many others there are likely to oppose the House plan.

"I'm leaning no. The Granger report is constructive, but no one has come up with a plan for how to deal with the Senate," King said. "We're putting our head in the noose and associating ourselves with the president's problem. This is man caused disaster and the man who caused it is Barack Obama."

King and his aides served Chick-Fil-A breakfast items and coffee at the meeting, which was held in a conference room on Capitol Hill.

Cruz, who is said to be mulling a 2016 presidential bid, has previously huddled with House Republicans on several occasions, including over Mexican food at Tortilla Coast during last year's federal government shutdown.