"This strategy of the president's automatic cuts borders on untruthful."

As an example, Olson cited a statement from the Federal Aviation Administration that warned more than 200 airports are at risk of closing due to the sequester. But he said the FAA admitted that only about 100 airports would actually be closed.

"It's Mayan politics," he said. "Two hundred thirty eight affected airports puts more fear in people than 100 regional airports."

Other Republicans have noted that the Obama administration has some control over what federal programs would be cut, and they have accused Obama of furloughing hundreds of thousands of workers in order to make the cuts as painful as possible. This plan, they said, seems designed to try to convince the public to maintain current spending levels.

The Mayan calendar is routinely pointed to as a predictor of the end of the world, although many experts believe — and are routinely proven correct — that the calendar is being misinterpreted when it is used this way. The last time the world was supposed to end was December 21, 2012.