By Anne Flaherty and Julie PaceWASHINGTON -- President Barack Obama and House Speaker John Boehner met Sunday at the White House to discuss the ongoing negotiations over the impending "fiscal cliff," the first meeting between just the two leaders since Election Day. Spokesmen for both Obama and Boehner said they agreed to not release details of the conversation, but emphasized that the lines of communication remain open. The meeting comes as the White House and Congress try to break an impasse over finding a way to stop a combination of automatic tax increases and spending cuts scheduled to kick in at the beginning of next year. Obama met in November with Boehner, as well as Senate Majority Leader Harry Reid and House Minority Leader Nancy Pelosi. The president spoke by telephone with Reid and in person with Pelosi on Friday. Obama has been pushing higher tax rates on the wealthiest Americans as one way to reduce the deficit -- a position Boehner and other House Republicans have been steadfastly against. Republicans are demanding steeper cuts in costly government entitlement programs like Medicare and Social Security. One GOP senator said Sunday that Senate Republicans would probably agree to higher tax rates on the wealthiest Americans if it meant getting a chance to overhaul entitlement programs. The comments by Bob Corker of Tennessee -- a fiscal conservative who has been gaining stature in the Senate as a pragmatic deal broker -- puts new pressure on Boehner and other Republican leaders to rethink their long-held assertion that even the very rich shouldn't see their rates go up next year. GOP leaders have argued that the revenue gained by hiking the top two tax rates would be trivial to the deficit, and that any tax hike hurts job creation. But Corker said insisting on that red line -- especially since Obama won re-election after campaigning on raising tax rates on the wealthy -- might not be wise. "There is a growing group of folks looking at this and realizing that we don't have a lot of cards as it relates to the tax issue before year end," Corker told "Fox News Sunday."