The Senate is coming dangerously close to legislating, with Senate Minority Leader Mitch McConnell (R-Ky.) announcing today that Republicans support the Democratic jobs bill currently on the floor.

The bill “is something we support and look forward to passing,” McConnell said on the Senate floor.

He added that the measure has been “championed by [Republican] Sen. Scott Brown of Massachusetts and would help contractors who do business with the government.” The measure would repeal a law that requires federal, state and local governments to withhold 3 percent of nearly all of their contract payments beginning in 2013.

McConnell also said he was “glad to see” that Democrats want to offer an amendment that would provide tax incentives for hiring unemployed veterans — similar to a provision in President Barack Obama’s jobs plan — and job training initiatives for unemployed veterans. The cost of the amendment would be offset by the extension of fees set to expire as part of a veterans’ mortgage program.

“This is just the kind of thing we’ve been calling for, just the kind of thing we should be doing a lot more of around here,” McConnell said.

The withholding mandate is intended to go after scofflaw government contractors who avoid paying taxes, but supporters of the repeal argue that it would impose significant financial burdens on both the public and private sectors. The repeal also appears to have the support of Obama, who included a one-year delay of the measure taking effect in his jobs package.

A similar measure offered by Senate Republicans fell three votes short of advancing Oct. 21 because of Democratic opposition to how it would be offset. The earlier bill would have rescinded $30 billion from fiscal 2012 discretionary spending, while the pending House-passed measure would pay for the $11 billion cost in lost tax revenue by closing a loophole in the health care overhaul law. Republicans argue that the loophole would allow some middle-class Americans to qualify for Medicaid.

Republicans have been critical of Democrats who, after not winning GOP support for the entire Obama jobs proposal, have sought to bring up pieces of the president’s jobs package individually and pair them with taxes on millionaires to offset their costs. The GOP contends that’s an effort geared more toward making Republicans looks like obstructionists rather than legislating.

“It appears the message may finally be breaking through,” McConnell said, adding that House GOP jobs bills have languished in the Senate and deserve to be considered.

His comments came after Senate Majority Leader Harry Reid (D-Nev.) said there was no reason Republicans should oppose the legislation and questioned why they had not come out in favor of it.

“There are no procedural or philosophical hurdles to passing this bill,” Reid said on the floor Tuesday.

“So I call on the Minority Leader and the rest of my Republican colleagues to break the silence,” Reid continued. “I ask my Republican colleagues, ‘Do you believe we should lend a helping hand to those who defend our freedom? Or do you think this nation’s responsibility to its veterans ends the day they take off the uniform?’”