WASHINGTON—South Carolina Republican Sen. Jim DeMint, as well as other conservatives, just gave Democrats a shiny new talking point.

The tea party-backed senator on Tuesday slammed House Republican leaders for the "fiscal cliff" proposal they offered earlier this week.

"Speaker [John] Boehner's $800 billion tax hike will destroy American jobs and allow politicians in Washington to spend even more, while not reducing our $16 trillion debt by a single penny," DeMint said in a statement. "This isn't rocket science. Everyone knows that when you take money out of the economy, it destroys jobs, and everyone knows that when you give politicians more money, they spend it. This is why Republicans must oppose tax increases and insist on real spending reductions that shrink the size of government and allow Americans to keep more of their hard-earned money."

Republican House leaders on Monday sent a letter to the White House with a plan to avoid a series of automatic tax increases and spending cuts set to begin on Jan. 1, 2013. With a 10-year price tag of about $2.2 trillion, the Republican proposal would raise federal revenue by closing loopholes and capping deductions within the tax code and making changes to entitlement programs. The letter was signed by seven House leaders, including Budget Committee Chairman Paul Ryan of Wisconsin and Ways and Means Committee Chairman Dave Camp of Michigan.

Democrats dismissed it quickly, calling for a bill that would increase taxes on households earning more than $250,000 per year and more federal spending on infrastructure, which were not included in the Republican plan.

Other conservatives have panned the proposal as well, with the Heritage Foundation releasing a blunt analysis. "Rarely in modern American politics have more counterproductive, more foolish words been set to paper," wrote Heritage Foundation researchers.

And in an open letter signed by more than 100 prominent conservative activists and organized by the advocacy group Let Freedom Ring, House Republicans were warned that they could lose support if they "cave" during negotiations.

As for DeMint, his comment may be a bit of a sideshow—he's not directly involved in the negotiations and he represents just a single vote in Congress—but it's representative of how conservatives feel about the Republican proposal, and it offers ample ammunition to President Barack Obama and Democrats in the fiscal cliff media relations war.