The Senate is expected to vote on the measure either late Tuesday or early Wednesday.
In his statement, Mourdock also said Lugar "switched course" on repeal of the military's "don't ask, don't tell" policy "when the threat of my candidacy was rumored."
Mourdock is waging a Tea Party-backed primary challenge to Lugar and has already rolled out the backing of a majority of Indiana Republican county chairmen from across the state. Tea Party groups are pointing to Lugar as their number one 2012 target.
Last week, Sen. Dan CoatsDaniel (Dan) Ray CoatsOvernight Hillicon Valley — Scrutiny over Instagram's impact on teens Former national security officials warn antitrust bills could help China in tech race Cyber preparedness could save America's 'unsinkable aircraft carrier' MORE (R-Ind.) and Rep. Mike Pence (R-Ind.) said they would remain neutral in the primary, dealing another early blow to Lugar, something Mourdock touted in a fundraising appeal late last week.
Lugar told CNN on Monday that he already has "boots on the ground," organizing ahead of 2012.
Lugar did say Tuesday that he does not like the "formulation" of the spending cuts passed by the House and would like Congress to go even further to cut the deficit."
Last month, Lugar raised concerns about the House bill during an interview with CNN. Lugar said then that he would "not support the entirety of the House bill."