WASHINGTON — A modest, bipartisan budget pact designed to keep Washington from lurching from fiscal crisis to fiscal crisis and ease the harshest effects of automatic budget cuts is on the brink of passing the Senate.

The Senate is on track to clear the bill Wednesday for President Barack Obama’s signature after a 67-33 vote Tuesday in which it easily hurdled a filibuster threshold.

The measure would restore $45 billion, half the amount scheduled to be automatically cut from the 2014 operating budgets of the Pentagon and some domestic agencies, lifting them above $1 trillion. An additional $18 billion for 2015 would provide enough relief to essentially freeze spending at those levels for the year.

The bill advanced Tuesday with the help of 12 Republicans, several of whom promised to oppose the measure in Wednesday’s final vote because it fails to take on the nation’s most pressing fiscal challenges. It would barely dent deficits that are predicted to lessen in the short term but grow larger by the end of the decade and into the next.

One provision, cutting the inflation increases of pensions for military retirees under the age of 62, was proving to be especially unpopular. Members of the military are eligible to retire after 20 years at half pay. The provision was included in the bill at the direction of House Budget Committee Chairman Paul Ryan, R-Wis.

Top Democrats said they would revisit the cut, which raises $6 billion over 10 years, before it takes effect in two years. Senate Budget Committee Chairman Patty Murray, D-Wash. — Ryan’s negotiating partner on the budget agreement — was grilled by Sen. Roger Wicker, R-Miss., on whether she knew the cut could reduce by $80,000 the lifetime benefit of a soldier who retires in his or her early 40s.

“I would suggest the senator ask that question to Chairman Ryan,” Murray said. In a document defending the cut, Ryan’s staff called pensions to middle-aged military retirees “an exceptionally generous benefit, often providing 40 years of pension payment in return for 20 years of service” and noted that “most begin a second career after leaving the military.”

“This bipartisan bill takes the first steps toward rebuilding our broken budget process. And, hopefully, toward rebuilding our broken Congress,” Murray said.

Sen. Jeanne Shaheen, D-N.H., who faces a potentially tough re-election campaign next year, promptly announced she would seek to repeal the military pension cut. The proposed pension cut has drawn howls of protest from senators with large military presences in their states.

“I promise you this. If we don’t fix it now, not only are we going to review it, we are going to fix it,” Sen. Lindsey Graham, R-S.C., said. “How could any commander in chief sign a bill that does this?”

Shaheen was joined by more than a dozen other Democrats in announcing legislation to restore the military retirement benefits and make up the money by closing a tax loophole on offshore corporations.