The Senate on Tuesday advanced legislation that would extend federal unemployment benefits to more than 1 million jobless Americans despite Republican demands that the $6.4 billion price tag be offset by budget cuts.

The 60-37 vote was just enough to clear the parliamentary hurdle and open debate on the measure. The measure advanced when a handful of Republicans joined Democrats in backing it.

Even if the Senate passes the bill, it will likely sit in limbo unless the Republican House and Democratic Senate negotiate a way to offset the cost without adding to the debt or deficit. House Speaker John Boehner, R-Ohio, signaled Tuesday that he is unwilling to consider an extension of benefits if the cost is not offset elsewhere in the budget.

The benefits extension should also include job-creating provision, Boehner said in a statement following Tuesday's vote.

"One month ago, I personally told the White House that another extension of temporary emergency unemployment benefits should not only be paid for but include something to help put people back to work," Boehner said. "To date, the president has offered no such plan. If he does, I’ll be happy to discuss it, but right now the House is going to remain focused on growing the economy and giving America’s unemployed the independence that only comes from finding a good job.”

Federal unemployment insurance expired Dec. 28, cutting payments to 1.3 million Americans who have been jobless for more than 26 weeks.

Senate Democrats used the debate over jobless benefits to highlight income inequality, a central part of the party's political strategy going into the 2014 elections.

In urging passage of the bill, Senate Majority Leader Harry Reid, D-Nev., told the story of his car ride into work on Tuesday, when temperatures in capital dipped into the single digits. Reid said he spotted a homeless person wrapped in blankets on Constitution Avenue, just a dozen blocks or so from the Capitol and the White House.

"The rich are getting a lot richer and the poor are getting a lot poorer, and the middle class are being squeezed," he said. "These benefits make the difference between being able to live a decent life and being hungry and becoming homeless."

Republicans, meanwhile, said offsetting the cost of any new benefits would help rein in federal spending, which in turn would improve the economy and create jobs so that unemployment benefits would not be needed.

"There is literally no excuse to pass unemployment insurance without also finding ways to create good, stable jobs and also finding the money to pay for it," Senate Minority Leader Mitch McConnell, R-Ky., argued before the vote.

McConnell proposed an amendment to the extension -- quickly rejected by Reid -- that would have have paid for the benefits by delaying the individual mandate called for in Obamacare, a money saver according to the non-partisan Congressional Budget Office.

Reid called McConnell's proposal "a guise to obstruct" the legislation, noting that no offsets were used in the vast majority of more than a dozen benefit extensions Congress granted over the past five years.

But Republicans are likely going to continue to insist on paying for the extension as the debate on the bill continues Tuesday.

The bill still must pass another 60-vote hurdle to end debate and advance to a final vote, and Republicans could use leverage they have on that vote to insist on offsets.

It's likely they will do so, particularly in the face of pressure from outside conservative groups like Heritage Action and Club for Growth, which oppose the extension.

Democrats making the case to extend benefits are walking a political tightrope as they try to demonstrate the economy is both recovering under President Obama but still in bad enough shape to warrant jobless pay.

The nation's current jobless rate has steadily decreased in the past year to 7 percent. But in 22 states, jobless rates exceed that national average, going as high as 9 percent in places as diverse as Nevada and Rhode Island.

"It's clear the economy is picking up steam, but for far too many Americans, these bright headlines touting good economic news don't match the dark reality of their lives," Reid said.

Obama, who supports an extension, was scheduled to address the issue Tuesday.

The half-dozen GOP senators who voted open debate on the bill are: Susan Collins of Maine; Kelly Ayotte of New Hampshire; Lisa Murkowski of Alaska; Rob Portman of Ohio; Dan Coats of Indiana; and bill co-sponsor Dean Heller of Nevada.