NBC News/Wall Street Journal poll found that 76 percent of Americans consider it unacceptable to cut Medicare, while 67 oppose cutting Medicaid, despite their deficit concerns.

Cantor also told NPR last week that it simply wasn't possible for America's most beloved entitlement programs to survive.

"We're going to have to come to grips with the fact that these programs cannot exist if we want America to be what we want America to be," he said.

"Eric Cantor's statement underscores that, now, [Republicans] are willing to turn on seniors by taking away the very bedrock of their financial and health security," Rep. Jan Schakowsky's (D-IL) said during at Thursday conference call.

"With all due respect, what the Congresswoman is saying is simply untrue -- Eric has made clear for months that he is committed to ensuring the long-term viability of these programs by addressing their solvency issues now," Cantor spokesman Brad Dayspring told Raw Story.