Senate Democrats say the next piece of President Obama’s $447 billion jobs package they will attempt to advance in the Senate is a measure to offer businesses tax incentives for hiring unemployed veterans.

But they said they will not seek to pay for the bill with increased taxes on millionaires — as they have with other failed pieces of the president’s plan — in an overture to Republicans geared toward actually getting the bill passed.

Since Republicans blocked consideration of the American Jobs Act last month, Democrats have been conducting show votes on individual elements of the plan, including $35 billion in state aid for hiring teachers and first responders and $60 billion for infrastructure improvements.

Their goal has been to show that Republicans are obstructing Obama’s ideas to improve the economy.

Republicans said those measures were designed to fail because Democrats proposed paying for them with higher taxes on people making more than a $1 million a year, which they knew the GOP would oppose. Democrats countered that those who are doing best in a difficult economy could afford to pay a little more to help others.

But Democrats signaled Friday that they might be looking to break the logjam on a veterans hiring bill, the piece of Obama’s plan that has always enjoyed the broadest bipartisan support.

In a conference call with reporters, Sen. Debbie Stabenow (D-Mich.), Sen. Jon Tester (D-Mont.) and Sen. Patty Murray (D-Wash.) said the measure would strengthen programs that help service members make the transition to civilian life and instruct the Labor Department to look for ways to make it easier for veterans to get civilian professional certification for jobs they learned in the military.

“No veteran should stand at the back of any line, and certainly not an employment line,” Stabenow said.

The measure groups together several veteran-related initiatives, including a proposal to provide hiring tax credits similar to those proposed by Obama.

The bill would offer businesses a tax credit of up to $9,000 if they hired a disabled veteran who had been out of work for more than six months. They could get a $5,600 credit for hiring any veteran unemployed for at least six months and $2,400 for hiring a veteran out of work for at least a month.

Earlier this month, the House passed a measure that would provide additional job training for veterans, and the senators said they were eager for GOP support.

“This is an issue that shouldn’t be partisan,” Tester said.

And Democrats’ decision not to attach the millionaires surtax they have been urging with other parts of the president’s package could help. Murray said the bill would be funded through existing Department of Veterans’ Affairs spending — adjusting fees for home loans offered by the department.

Democrats will likely move to tack the veteran’s bill onto another measure under Senate consideration next week that also enjoys bipartisan support — a bill that will repeal a 3 percent withholding fee on government payments to vendors that had been set to take effect in 2013.