Mississippi Gov. Haley Barbour (R) criticized the Tea Party wing of the GOP on Tuesday for failing to get behind Republican leadership on a deficit plan.

"Our people have to understand that we can't let the perfect be the enemy of the good," Barbour said.

Barbour said House Speaker John Boehner (R-Ohio) had shown "courage" in the deficit debate by agreeing to compromise in order to raise the debt ceiling.

"In politics, purity is a dead-dog loser," he said. "We cannot go out with the idea that we're going to be pure, or we're going to do nothing."

Speaking on conservative Laura Ingraham's radio show, Barbour warned that only compromise would produce a "good" deficit deal.

"If I had my way, if I were a dictator, we'd have no tax increases," he said. "But Republicans control one half of one third of the government."

Barbour said Tea Party Republicans such as Sen. Jim DeMint (S.C.) needed to get behind Boehner's effort, rather than clinging to the "cut, cap and balance" Act that passed the House but "isn't going anywhere in the Senate."

DeMint on FOX News Monday evening criticized Boehner's plan as "essentially the same thing" as Senate Majority Leader Harry Reid's (D-Nev.) plan. He also tweeted that both plans "are political deals, not debt solutions."

The two-step plan offered by Boehner on Monday would raise the debt ceiling by $1 trillion for a few months and make $1.2 trillion in cuts as the first step. Step two would be to appoint a commission to recommend additional deficit-reduction proposals for Congress to vote on and require a vote on a balanced-budget amendment to the Constitution.

DeMint pledged to continue working to pass the Cut, Cap and Balance Act, which conditions raising the debt ceiling on immediate spending cuts, capping annual spending and voting on a balanced-budget amendment.

The Cut, Cap and Balance Coalition, representing more than 100 Tea Party and conservative activist groups, also on Monday released a statement opposing Boehner's plan. The group said it could not support Boehner in part because it feared a congressional commission would "make it easier to raise taxes than to institute enduring budget reforms."

However, the Tea Party movement could be more divided in its response on a local level. One local group in Boehner's home district organized a rally to show support for the Speaker on Monday that drew a crowd from southwest Ohio and northern Kentucky, according to the Cincinnati Enquirer.

Ingraham, who urged her viewers to call DeMint and other Republicans and tell them to support Boehner's plan, said she agreed with Barbour's message that Tea Party leaders needed to be told, "Don't stab your guy in the back."