The bill will likely have great difficulty moving in the Democratic-led Senate. But Thune's office said companion legislation is expected to be introduced next week by House Republican Conference Chairman Jeb Hensarling (R-Texas) and Budget Committee Chairman Paul RyanPaul Davis RyanRyan, GOP lawmaker trade 'bad dad jokes' ahead of Father's Day Hugh Hewitt to Trump: 'It is 100 percent wrong to separate border-crossing families' White House walks back Trump's rejection of immigration compromise MORE (R-Wis.).

Passage is much more likely in the GOP-led House, which would give Republicans more leverage to argue for clarity from the administration, something they said has not been forthcoming even though sequestration cuts must be made under current law starting in January.

"After providing conflicting statements about how the cuts will be levied, the Obama administration needs to provide a transparent plan to Congress and the American people detailing their proposal for the sequestration cuts," Thune said Wednesday. "My bill would simply require the Obama administration to be transparent when making these spending cuts, just as would be required under a normal budget process."

Republicans have argued for months that while the Obama administration says it fears the effect of cuts to defense spending, it has offered no proposals to get around these required cuts.

According to the bill, the administration's report to Congress would have to estimate the percentage cuts to each discretionary program needed to implement the sequester, and name each account that would get hit by the sequester.

Earlier this month, House Republicans approved their alternative to deep defense cuts, by passing the Sequester Replacement Reconciliation act.