House Republican leaders put forward a measure they’ve pushed out before, a bill to replace the sequester with new spending reductions, as a way to offset part of the cost of the fiscal deal that the Senate sent to the House early Tuesday morning.

According to lawmakers and aides, House GOP leaders were looking for 218 votes to attach the earlier measure as an amendment to the Senate bill, perhaps as soon as Tuesday evening.

The sequester bill (HR 5652) passed the House 218-199 largely along party lines in May but was never taken up by the Senate. It would have replaced the first year of a 10-year, $1.2 trillion package of defense and other discretionary program cuts with a $19 billion reduction to discretionary caps for fiscal 2013 and a $310 billion cut over a decade to mandatory programs such as Medicaid and food stamps.

The bill also would have increased by 5 percent the amount that federal employees pay into their pension plans, saving the government $2.3 billion in fiscal 2013. It also would have abolished the Federal Deposit Insurance Corporation’s ability to break up failing financial institutions, eliminated assistance to homeowners through the Home Affordable Modification Program and raised premiums on subsidized flood insurance policies.

All told, the amendment would represent a $330 billion reduction in the budget.

Several conservatives, however, said the amendment would not represent enough of a spending cut to offset the Senate fiscal cliff bill, which the Congressional Budget Office says would add nearly $4 trillion to deficits.

“There’s not enough cuts,” said Rep. Louie Gohmert, R-Texas. “$30 billion a year when we’re increasing the deficit by $4 trillion.”

At a Tuesday afternoon Republican Conference meeting, members also discussed cutting back on a package of tax extenders included in the Senate bill to wring some additional savings, but they decided against that, said Rep. Kenny Marchant, R-Texas.

Many lawmakers predicted leaders would not get the 218 votes needed to move the sequester replacement bill as an amendment.

Despite the objections of conservatives, other Republicans simply wanted to vote on the Senate bill without amendment, said Jack Kingston, R-Ariz. That combination should be enough to ensure there will not be a vote on the amendment, he said.

Rep. Dennis A. Ross, R-Fla., who supported the amendment, also predicted House leaders would not get the 218 votes needed.

“If they don’t have the 218, they will bring up the Senate bill for an up-or-down vote,” he said.

He expected the Senate bill would pass, sending the measure on to the president.