(CNNMoney) -- Heading into Veterans Day, the Senate unanimously passed a bill to help unemployed veterans seeking jobs as well as federal contractors facing a new tax burden in 2013.
The Senate voted 95-to-0 Thursday to pass the first and so far only piece of President Obama's jobs package to get out of the chamber. The House is expected to take up the bill and pass it next week.
Lawmakers are touting the bill as a bipartisan jobs creator that is fully paid for and would even reduce federal deficits by $2 billion over the next decade, according to the Congressional Budget Office.
"The bills won't solve our jobs crisis," said Senate Minority Leader Mitch McConnell on Thursday. "But this attempt at bipartisanship has been used to help get them over the finish line and represents our best shot at making progress on jobs in the economy."
The bill gives employers tax credits of up to $5,600 for hiring veterans who have been unemployed longer than six months. It would also give employers a tax credit of up to $9,600 for hiring long-unemployed disabled veterans.
The October unemployment rate for veterans who left the military after 2001 was 12.1%, leaving about 240,000 veterans out of work, according to the White House. The measure to help veterans is a small piece of President Obama's job package.
"Let's work together to get this bill passed, because it's the least we can do for those whom we owe so much," said Sen. Jon Tester, a Montana Democrat and sponsor of the veterans' measure.
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The bill also expands an education and jobs retraining program for unemployed veterans. And it creates a new project that directs the Labor Department to figure out ways for veterans to use their specialized training to get licenses in different fields in the civilian work force.
Republican Jim DeMint of South Carolina was the only lawmaker who voted against the amendment adding the veterans measure to the bill, saying he didn't think the government programs for veterans work. But, he voted in favor of then overall bill with the veteran tax credits on final passage.
Maine Republican Olympia Snowe voted "present" on the bill.
The Senate plans to pay for the tax credits by keeping special fees that the Department of Veterans Affairs charges veterans for guaranteeing mortgages at current levels. Those fees had been scheduled to get cheaper for veterans. By keeping the fees at current levels, the federal government can tap that revenue stream.
The bill also repeals a George W. Bush-era tax accountability law that would have allowed the federal, state and local governments to withhold 3% of contractor pay, allowing those dollars to be applied as a credit toward federal income taxes. That law was supposed to take effect on Jan. 1, 2013.
Congress initially passed the withholding requirements back in 2006 to ensure that the government collected all taxes owed by contractors. Big business groups, including the U.S. Chamber of Commerce, have been pushing to repeal the measure.
The House overwhelmingly passed that bill last month with a vote of 405-16.
The cost of repealing the tax withholding measure is about $11 billion. Congress would pay for the repeal by changing a part of the new health care reforms. The government would redefine who is eligible for federal help under new health care reforms, making it more difficult for some to qualify for Medicaid or subsidized health care coverage.
The bill raises the threshold level to qualify for government help by including nontaxable Social Security benefits, as well as the taxable portion, as income.
The White House issued a statement on Thursday supporting the measure, saying it would "reduce unemployment and ensure that our veterans leave the military with the tools they need to succeed in the civilian workforce."