House Speaker John Boehner introduced the GOP's deficit-reduction proposal Monday, but not all Republicans are fully behind the offer--including the president of the conservative group FreedomWorks.

"I think (Boehner) is negotiating with himself," Matt Kibbe told CNN on Tuesday. "I wish Republicans would lay out a more substantial vision."

The GOP plan promises $2.2 trillion in deficit savings over the next decade, including $800 billion in revenue from tax reform, $600 billion from Medicare reforms and other health savings and $600 billion in other spending cuts.

It also pledges $200 billion in savings by revising the consumer price index, a measure of inflation.

Republicans said the offer is based on a proposal last year by Erskine Bowles, a Democrat who co-chaired a bipartisan deficit-reduction panel appointed by Obama in 2010. Bowles, however, discounted the GOP plan Monday, saying it reflected his view a year ago but "circumstances have changed since then."

For his part, Kibbe said the plan does not go far enough in spending cuts. The fiscal conservative said Republicans "are getting away with murder" because they're not offering "specifics" in entitlement cuts. "I think Boehner is at risk of splitting his caucus," he added.

The GOP plan, however, did delve into some details Monday, by offering to raise the eligibility age for Medicare, for example.

Kibbe also took issue with efforts to forestall the sequester, a massive amount of spending cuts ($1.2 trillion) set to start kicking in at the beginning of next year if Congress fails to reach an agreement. Whether or not they come up with a plan, Kibbe argued the cuts should still happen.

"They've got to cut spending. These are nominal cuts, these are not draconian cuts," Kibbe said. "This is a slight haircut."

His comments come as the group faces a high-profile departure from its former chairman, Dick Armey, who recently resigned.