The Senate has agreed to proceed to a full debate on a measure to repeal a tax provision that both parties believe would burden government contractors if allowed to go into effect in 2013.

The overwhelming 94 to 1 vote to allow the measure to move forward marks the first time a piece of President Obama’s $447 billion jobs package, albeit a small sliver, has cleared the 60-vote procedural hurdle necessary for full consideration in the Senate.

The Senate will now consider amendments to the legislation, and Democrats have indicated they will add another piece of Obama’s jobs bill in coming days: tax credits for businesses that hire veterans.

Both pieces of the bill could receive bipartisan support in votes this week, particularly because Democrats have not attempted to fund either through a surtax on those making more than a million dollars a year, as they have with other pieces of Obama’s jobs bill that Republicans have blocked in recent weeks.

The 3 percent withholding proposal that forms the base of the bill advanced Monday represented a tiny portion of Obama’s package, which was dominated by proposals to extend the payroll tax holiday for workers, provide new federal funding for infrastructure improvement, provide aid to states to hire teachers and first responders, and create tax credits to encourage businesses to hire the long-term unemployed.

But Obama did also recommend postponing the scheduled 2013 implementation of a new tax provision that would require federal, state and local governments to withhold 3 percent of payments to their vendors.

Republicans have accused Democrats of advancing pieces of the president’s plan sure to draw opposition so they could paint the GOP as resistent to Obama’s jobs ideas. They have urged Senate Democrats to move ahead with the 3 percent withholding bill for several weeks and applauded their decision to do so Monday.

“For nearly three years, President Obama has demanded that we pass massive legislation he knows Republicans have problems with. What we’re saying is, let’s start with things that have bipartisan support, that we know can pass, instead,” Senate Minority Leader Mitch McConnell (R-Ky.) said Monday.

Congress had adopted the withholding rule in 2005 as a way to ensure that government contractors were paying their taxes. The idea was that contractors would receive a refund if their tax bill totaled less than 3 percent.

But contractors immediately complained the withholding would disrupt their cash flow and crush their business. The rule’s implementation had been delayed twice already.

Senate Republicans and a few Democrats joined last month to block consideration of the president’s full jobs plan and then, again, stymied consideration of planks of the plan to provide funding for teacher hiring and infrastructure spending.

But the withholding legislation is likely to fare better. The GOP-led House has already passed a bill repealing the withholding rule and proposed funding it by slightly restricting eligibility for Medicare and Medicaid.

In coming days, debate on the bill is likely to shift to amendments to the measure, including one dealing with veterans, which will also provide new funding for programs to help service members transition to the civilian workforce.

The House passed a similar measure to help veterans in October. The chairmen of the House and Senate Veterans’ Affairs committees — Sen. Patty Murray (D-Wash.) and Rep. Jeff Miller (R-Fla.) — offered bipartisan backing for the Senate proposal Monday.

Obama also urged Congress on Monday to adopt tax credits to encourage businesses to hire veterans.