WASHINGTON  After clamoring loudly about their plans to curtail federal spending, House Republicans announced Thursday that they would cut $32 billion for the remainder of the fiscal year  a minuscule amount compared with a projected annual deficit of nearly $1.5 trillion.

The Republican proposal is effectively $58 billion less than the domestic and foreign aid programs in President Obama’s budget request for 2011  far short of the $100 billion in cuts that Representative John A. Boehner promised before the November elections that catapulted Republicans into the House majority and made him the speaker.

Republicans said that their cuts, prorated for the balance of the fiscal year, still fulfilled their campaign pledge to reduce to 2008 levels the government’s discretionary spending on everything other than national security. They said that the Democrats’ failure to approve a budget or pass any of the normal spending bills precluded further cuts.

But their unwillingness to impose steeper reductions also reflected the severe difficulty they face in slashing spending on the wide scale demanded by some Republicans, especially Tea Party-backed freshmen elected partly on a promise of fiscal restraint.