WASHINGTON, DC : On Monday, Senator Orrin Hatch (R-UT), pictured here in 2012, along with Senator Johnny Isakson (R-Ga.) added their names to a growing list of Republican sentators who declared their support for the bipartisan deal. (Bill O'Leary/WASHINGTON POST)

Despite a concerted attack by conservative advocacy groups, a bipartisan deal to roll back sharp spending cuts known as the sequester appeared on track to clear the Senate after a growing number of Republicans declared their support for the measure.

On Monday, Sens. Orrin G. Hatch (Utah) and Johnny Isakson (Ga.) added their names to a list that included Sens. John McCain (Ariz.), Susan Collins (Maine) and Ronald H. Johnson (Wis.).

At least two others who were undecided on the substance of the agreement said they will nonetheless help the Senate’s 55 Democrats assemble the 60 votes needed to clear a critical procedural hurdle Tuesday morning.

The federal budget accord “isn’t everything I’d hoped it would be, and it isn’t what I would have written,” Hatch said in a statement. “But sometimes the answer has to be yes.”

The deal, struck by Senate Budget Committee Chairman Patty Murray (D-Wash.) and House Budget Committee Chairman Paul Ryan (R-Wis.), is intended to end nearly three years of acrimony over the budget in Washington. It would cancel half the sequester cuts for the current fiscal year, replace them with other savings and allow Congress to avert another government shutdown in January.

Last week, the agreement sailed through the House on a vote of 332 to 94, raising hopes that Republicans were finally drawing to a close an era of uncompromising confrontation over the budget. But trouble quickly cropped up in the usually more moderate Senate, where a slew of tea party heroes — and GOP incumbents facing tea-party challengers — lambasted the deal.

Following the lead of outside groups such as Heritage Action for America and the Club for Growth, several Republican senators complained that the agreement would allow agency spending to rise over the next two years in exchange for the vow of spending reductions nearly a decade from now.

“It increases spending by $60 billion over the next two years but promises to pay for it with cuts over the next 10 [years] — something that we know Congress never gets back to actually carrying out,” said Sen. Marco Rubio (Fla.), a possible contender for the 2016 GOP presidential nomination.

More worrying for advocates of the agreement, two key Republican allies in the fight against the sequester — Sens. Lindsey O. Graham (S.C.) and Kelly Ayotte (N.H.) — said late last week that they, too, would vote against the measure. Although the agreement would cancel a hit to the Pentagon budget set for January, an outcome Graham and Ayotte have been campaigning for months to prevent, the pair complained that the deal also would dial back cost-of-living increases for the youngest military retirees.

“It’s unacceptable to single out our men and women in uniform in this way,” Ayotte said.

Some Democrats, meanwhile, were grumbling that the deal includes no provision for extending unemployment insurance for the long-term jobless. Those benefits are set to expire at the end of December, cutting off 1.3 million people.

Although senior Senate aides never doubted their ability to assemble the 50 votes needed to pass the agreement, their ability to get 60 votes to squash a threatened GOP filibuster seemed less certain. So Murray and Ryan worked through the weekend to shore up support. House Speaker John A. Boehner (R-Ohio) also reached out privately to a few of his closest friends.

By Monday morning, the tide had turned, and Sen. Charles E. Schumer (N.Y.), the No. 3 Democrat in the Senate, said on MSNBC that it is “safe to say” the measure will pass the chamber. A final vote could come as soon as Tuesday evening, if Senate Republicans agree to speed things up. Otherwise, the chamber is likely to send the measure to the White House late Wednesday.

The proposal would raise about $85 billion over the next decade through a variety of policies, including trimming pensions for civil-service workers and military retirees younger than 62, raising security fees for airline passengers and extending the sequester for Medicare providers an additional two years, through 2023.

About $62 billion of those savings would go to replace a portion of the sequester in fiscal 2014 and 2015, restoring spending for the Pentagon and domestic agencies. The rest of the savings, about $23 billion, would go toward trimming deficits projected to exceed $6 trillion over the next decade.

In announcing his support, Hatch said the agreement is “built on the necessary consensus that reflects divided government.”

“I appreciate the hard work of Paul Ryan, Speaker Boehner and House Republicans in crafting this commendable compromise that reduces our debt over the long-term, prevents another government shutdown, and stops the budget battles that have rocked America with economic uncertainty and political pessimism,” Hatch said. “Much more work needs to be done. . . . My hope is that this budget agreement paves the way to greater stability, lasting deficit reduction, and the political will to tackle those challenges in the near future.”