The U.S. Senate will vote in early January on temporarily extending unemployment insurance to millions of out-of-work Americans, Senate leaders said Thursday.

Majority Leader Harry M. Reid (D-Nev.) said that a bipartisan plan to extend the benefits for three months will get a vote on Jan. 6 or 7, the first two days the Senate is scheduled to meet in 2014.

"It's a good bill, and it deserves a vote, and I hope my Republican colleagues will work with us to schedule a vote in a very timely fashion, which to this point they haven't," he told reporters.

But Reid and said that extending unemployment insurance "is just the first step. We need to raise the minimum wage. We need to take other measures that will help address income inequality in this country. We have income inequality."

The bipartisan budget agreement overwhelmingly approved by lawmakers fails to extend the unemployment benefits for about 1.3 million long-term unemployed American workers. Dozens of House and Senate Democrats protested the oversight, but agreed to back the budget agreement after top Democratic leaders said they would take up the issue of extending the benefits in January.

Sen. Charles E. Schumer (D-N.Y.), the third-ranking Democrat, said the issue of extending unemployment benefits would be "the next test" in the ongoing battle between conservative and mainstream Republicans.

"They should be aware the tectonic plates of our politics are changing, because the decline of middle-class incomes and the difficulty in average people getting good-paying jobs has overtaken the deficit as the number one problem facing our political economy today," Schumer said, adding later that "issues like job creation, minimum wage and unemployment insurance are going to weigh on the minds of voters far more than Obamacare by the time the 2014 elections roll around."

Reid announced plans for the vote at a year-end news conference designed to focus on his 2014 priorities. But reporters also asked him whether he plans to make any changes to his leadership style after guiding through the Senate through its most unproductive year in history.

"I think about it a lot," he said, adding that he had met in recent days with Sen. Rand Paul (R-Ky.) to discuss several of the senator's concerns.

"I've grown to really like him," Reid said of Paul. "He's -- even though he has some set political views, he wants to get things done here. And I find that throughout the Republicans. I think they want to get things done. And I hope that's true. There are a number of people in the Republican side that are basically stopping everything. I need not give you names, but it's just a handful of people."