Nunnelee had joined a majority of GOP representatives in backing the plan put forth by House Speaker John Boehner. But plans for a Thursday evening vote on the measure ended abruptly before a decision could be reached.
According to media reports, Boehner didn't have enough votes to pass the plan and went in search of more support from Tea Party-oriented Republicans who say the plan doesn't cut spending enough.
The vote was postponed around 10 p.m. Thursday.
When contacted by the Daily Journal prior to the originally scheduled vote, Nunnelee said he would have preferred an earlier version of the spending plan that had been tabled last week by the U.S. Senate.
But "this plan avoids default, it stabilizes Social Security and makes sure checks go out," the Tupelo resident said. "And for the first time in history, it couples the increased debt limit with significant spending cuts."
The plan would raise the nation's $14.3 trillion debt limit by nearly $1 billion while cutting the deficit by $917 billion over the next decade.
Democrats, led by Senate Majority Leader Harry Reid, dislike the plan because it would require Congress to vote on another debt-ceiling hike during next year's presidential and congressional campaigns. They want the debt ceiling raised by the full $2.4 trillion President Barack Obama has requested, while cutting $2.2 trillion over a decade.
"I do believe the president is using Social Security as a scare tactic, and there may be a legitimate debate about what happens," Nunnelee said. "But if we move into Aug. 2, we move into uncharted territory, a place where we've never been."
Without a higher debt ceiling, the nation won't be able to borrow money to pay its bills - including Social Security payments, Medicare and Medicaid payments, defense vendors and federal employees - because existing revenues fall below expenditures.