A tiny piece of Obama’s jobs package just might have a chance of passing Congress.

The provision would give companies a tax credit of up to $9,600 for hiring veterans who’ve been unemployed for at least six months. The bill could come up for a vote in the Senate by the end of this week, and Republican Sen. Scott Brown (Mass.), for one, has already promised to sign on.

Veterans march to support the Occupy Wall Street movemet in New York earlier this month. (SOURCE: GETTY IMAGES )

What’s more, though the unemployment rate for recent Gulf War veterans “is quite high,” Indiviglio wrote, “the unemployment rate for veterans overall is relatively low -- just 7.7%.” Even if businesses did create a new job for each of these unemployed veterans—an unlikely best-case scenario— U.S. unemployment would drop from 9 to only 8.8 percent, he concluded.

Obama’s larger jobs plan contains a proposal that would give businesses a tax credit for job creating new jobs, rather than simply changing their hiring preferences. But the political divide over how to pay for the tax credit basically means that it’s going nowhere.