The Senate approved legislation that would repeal a law that would require federal, state and local governments to withhold 3 percent of nearly all of their contract payments beginning in 2013.

Approval of the bill, 95-0, came after the Senate attached an amendment to it that would provide tax incentives for hiring unemployed veterans. The amendment was approved on a 94-1 vote.

The Senate also voted 81-14 to move forward on a second package of appropriations bills, or minibus, which includes the State and foreign operations appropriations bill; the financial services and general government appropriations bill; and the Energy and water development appropriations bill. The Senate vote to cut off debate on the motion to proceed to the minibus sets up the chamber to begin debate on that package next week.

Sen. Patty Murray (D-Wash.), chairwoman of the Veterans Affairs Committee, said today she had received assurances that the GOP-controlled House would take up the tax and veterans bill. Similar legislation had passed through the House earlier this year.

The bill “takes a huge step forward in rethinking how we treat our men and women in uniform after they leave the military,” Murray said.

The cost of the amendment would be offset by the extension of fees set to expire as part of a veterans’ mortgage program.

Not all Republicans were in favor of the veterans’ amendment. Sen. Jim DeMint (R-S.C.), who was the only ‘no’ vote, said he believes all Americans should be treated equally by the tax code.

“I know what I am about to discuss won’t be very popular,” DeMint said. “I’ll probably be accused of not supporting veterans by politicians pandering for their votes, but I am not going to be intimidated to vote for something that may make political sense but is inherently unfair and won’t work.

“The best way to get veterans back to work is by doing the things that will help the economy and get all Americans back to work,” he continued.

The Senate’s passage of the underlying repeal bill capped a series of exchanges among the chambers and the administration that saw the Democratic-controlled Senate vote down a version of it, the GOP-controlled House pass a version and the Democratic White House support the GOP bill.

The withholding law was intended to go after scofflaw government contractors who avoid paying taxes, but supporters of the repeal argue that it would impose financial burdens on the public and private sectors.

President Barack Obama had included a one-year delay of the measure taking effect in his jobs package.

Before passing the measure, the Senate also defeated an amendment, 40-56, offered by GOP Sens. John McCain (Ariz.) and Rand Paul (Ky.) that mirrored the jobs package they unveiled last month. The amendment needed 60 votes to be attached to the tax bill.

“I think it’s very important that the American people know that there are different visions about how we would create jobs in this country,” Paul said on the floor today.

The plan would put a moratorium on regulations, repeal the health care and financial reform laws and streamline permitting for energy exploration and mining — all initiatives the GOP has been proposing all year.