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Sen. Bob Corker, R-Tenn. talks with reporters on Capitol Hill in Washington.

WASHINGTON - Sunday's political talk show circuit illustrated another deep divide at the Republican Party's highest levels, with a Tennessee senator promoting a balanced approach to America's defict and House Speaker John Boehner rejecting compromise in a partisan appeal to conservative budget slashers.

Striking a moderate tone, U.S. Sen. Bob Corker said he and other Senate Republicans are open to raising further tax revenue as part of a deficit reduction deal, calling a sweeping agreement possible a week after President Barack Obama's Capitol Hill visits.

"I think there, by the way, is a chance on a deal," the Tennessee Republican said on "Fox News Sunday." "I know the president is saying the right things, and we have an opportunity over the next four to five months."

Just as Corker opened a door to compromise, Boehner slammed it shut. He said House Republicans are rejecting all ideas for fresh tax revenue and would only consider spending cuts to close the nation's financial gap. The speaker appeared pessimistic at the chances for an elusive "grand bargain."

"I don't know whether we can come to a big agreement," Boehner said on ABC's "This Week."

Coming days after rising-star Sens. Marco Rubio and Rand Paul took veiled shots at Mitt Romney and John McCain at a national retreat for conservatives, the fiscal schism could undermine the GOP's efforts to unify for budget season, 2014 elections and beyond.

Corker said it will take a "75-year solution to entitlements" such as Medicare and Social Security to encourage Republicans to consider more tax revenue.

"I think Republicans, if they saw true entitlement reform, would be able to look at tax reform that generates additional revenue," Corker said. "And that doesn't mean increasing rates. That means closing loopholes."

Corker didn't identify specific loopholes, but Boehner shunned revenue talk altogether. He said "the president got his tax hikes on January 1," referring to the "fiscal cliff" deal that raised rates for individuals making more than $400,000 per year and households taking in more than $450,000.

"The talk about raising revenue is over," Boehner said.

Meanwhile, Corker expressed a willingness to collaborate with the president. The former Chattanooga mayor repeated his belief that Congress can't do it alone, imploring the president "or a designee" to maintain a physical presence on Capitol Hill.

Still, compromise seems a long way off, according to 10-year budget proposals released last week: House Republicans exclusively use spending cuts to narrow the deficit by $4.6 trillion, while Senate Democrats combine tax increases and cuts to slice the gap by $1.8 trillion.