More than a dozen House Republicans are putting new pressure on Congress to make cuts to discretionary spending in the next few years beyond those already agreed to under the summer debt-ceiling deal.

Rep. Marsha Blackburn Marsha BlackburnNetflix distances from author's comments about Muslim Uyghurs but defends project Hillicon Valley: Subpoenas for Facebook, Google and Twitter on the cards | Wray rebuffs mail-in voting conspiracies | Reps. raise mass surveillance concerns Key Democrat opposes GOP Section 230 subpoena for Facebook, Twitter, Google MORE (R-Tenn.) and others last week introduced legislation that would bring the discretionary spending levels in fiscal years 2013 and 2014 under the Budget Control Act to FY 2012 levels, saving $27 billion in those years. The bill has 13 co-sponsors, including two current members of the House GOP leadership: Majority Whip Kevin McCarthy (Calif.) and Republican Policy Committee Chairman Tom Price (Ga.).

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"Working class families around the country are continuing to tighten their belts, and they expect Washington to do the same," Blackburn said. "The spending caps that we have put in place are a great starting point, but more must be done to regain the trust of the American people."

Under the Budget Control Act, which reflected the August agreement to increase the federal debt ceiling, discretionary spending is capped at $1.043 trillion in FY 2012, a $7 billion cut from FY 2011 levels.

That same agreement calls for a cap of $1.047 trillion in 2013, and $1.066 trillion in 2014. But Blackburn's bill would reset those caps at $1.043 trillion.

The bill, H.R. 3043, likely has an uphill climb in the current Congress, as pressing it would essentially reopen the hard-fought August agreement to further negotiation. Still, it reflects a real GOP critique of that agreement, which cuts a total of about $10 billion in real spending in 2012 and 2013 before discretionary spending starts climbing above 2011 levels.

"The message from the American people is clear — STOP the madness," Blackburn said. "We have a moral obligation to take a stand for good government and work to protect the tax dollars of American workers.

"This bill builds on the momentum House Republicans have made this year, puts more controls on spending, and would help alleviate the debt burden currently weighing down our economy," she said.