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Republican Sen. Bob Corker acknowledged on Tuesday that consensus within the Republican and Democratic parties has become split as niche blocks pursue their own agendas.

"It is more like a parliament now based on people's interests," the Senate Foreign Relations Committee chairman told CNBC's "Squawk Box."

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Regarding his party, the Tennessee lawmaker said the GOP base has grown "very upset" throughout 6½ years of President Barack Obama's leadership. He said that dissatisfaction has intensified as the division of power in Washington has prevented Republicans from blocking some Democratic initiatives.

If a Republican is elected to the White House, Corker said, much of the fractiousness within his own party will dissipate. "If there are four years, or eight more years of Democratic leadership, I don't know where this goes."

The conservative grassroots and GOP donor base alike are "rightly" frustrated that Congress has not addressed the big issues weighing on American business, he added.

"I think sometimes the American people should be even more upset from my perspective, but it ought to be focused on long-term fiscal issues," he said. "Instead, it ends up a lot of times being about shiny objects that at the end of the day are not going to happen."

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Members of the tea party movement and the Freedom Caucus within the GOP recently threatened to shut down the government by vowing not to support any spending bill that funds Planned Parenthood. Lawmakers averted that outcome for the time being but face a December deadline over the country's long-term budget and debt limit.

The tea party and Freedom Caucus have also been seen as instrumental in the resignation of House Speaker John Boehner and the withdrawal of Rep. Kevin McCarthy's bid to win the speakership.