Tea party has too much GOP pull: Democrat Hoyer

Cantor defeat reveals 'deep divisions' in GOP: Rep. Hoyer

The primary defeat of House Majority Leader Eric Cantor shows how deeply divided and dysfunctional the Republican Party has become, when it comes to important issues like immigration reform, Minority Whip Steny Hoyer told CNBC on Thursday.

The perception of Cantor being too willing to compromise with Democrats on immigration has been blamed as a major factor in the Virginia Republican's stunning loss earlier this week.

"But the irony was Eric Cantor wasn't bringing immigration reform to the floor," Hoyer said in a "Squawk Box" interview.

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Cantor lost to tea party challenger David Brat "because the Republican Party is in the grips of its far-right element," Hoyer said, but he did still express hope that efforts to overhaul the nation's immigration law are not dead. The Maryland Democrat cited the willingness of House Speaker John Boehner, R-Ohio, to tackle the problem.

Not a triumph for tea party: Dick Armey

Dick Armey, who served as House Majority leader from 1995 to 2003, said Americans want immigration reform not amnesty, and a commitment to reforming and enforcing border security must come first.

Armey, a Texas Republican, also told "Squawk Box" that Brat's victory over Cantor should not be seen as a win for the tea party.

"No establishment tea party organization involved themselves in this race," he explained. "But you can call it a triumph for grassroots activism and grassroots campaigning over big money."

Cantor, a seven-term congressman, will be stepping down July 31 as House Republican leader—a position he's held since 2011. But Cantor's colleagues will vote to replace him next week.

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The No. 3 House Republican, Majority Whip Kevin McCarthy of California, is certainly looking for a promotion. But others want the job too, including Cathy McMorris Rodgers of Washington and a pair of Texas Republicans in Jeb Hensarling and Pete Sessions.

Whoever the Republicans choose will send a signal about the future of their party, Hoyer said.

Armey said the Republican Party should return to the message of late President Ronald Reagan, a conservative who was able to communicate his message to the American people without alienating his opponents.

—By CNBC's Matthew J. Belvedere.