The battle will kick off a 2014 drive by President Barack Obama and fellow Democrats to stem a growing gap between rich and poor.
The Democrat-led Senate plans to escalate the fight in coming weeks by bringing up for a vote a bill to increase the federal minimum wage, which has stood at $7.25 an hour since July 2009. Democrats want the minimum wage to rise over three years to $10.10 and then be indexed to inflation in the future.
"We are trying to catch up with what the American people have known for years - that they are working more for less," Democratic Senator Jack Reed of Rhode Island said in an interview.
Reed is a leading advocate of a minimum wage increase and, along with Republican Senator Dean Heller of Nevada, is sponsoring a bill to restore jobless benefits for 1.3 million Americans and prevent thousands more from soon losing such aid.
The Reed-Heller measure would extend for three months the Emergency Unemployment Compensation program, which ended on December 28 when its funding expired.
Signed into law in 2008 by Republican President George W. Bush, the program provided the jobless an average of $300 per week for an additional 28 weeks once state benefits ended.
Supporters argue that besides helping the unemployed, it boosts the economy as recipients quickly spend their benefit checks on essential goods, helping local retailers.
"Providing a safety net for those in need is one of the most important functions of the federal government," the conservative Heller said in a statement.
It is unclear if legislation to renew the 2008 emergency program or increase the minimum wage will muster the needed 60 votes in the 100-member Senate to clear procedural hurdles erected by Republicans.
But if they do, both can expect a steep climb in the Republican-led House of Representatives, which rejected most of Obama's largely liberal agenda the past three years.
Senate Majority Leader Harry Reid, a Nevada Democrat, on Sunday appealed to Republicans to allow the jobless benefit extension to pass.
"There are 55 of us (Democrats) and 45 of them (Republicans). It would seem to me that five Republicans in the Senate" could join Democrats to provide the necessary 60 votes, Reid said in an interview on CBS's "Face the Nation."
Obama also made an urgent pitch for Congress to act. On Saturday, in his weekly address, the president said Republicans should "make it their New Year's resolution to do the right thing and restore this vital economic security for their constituents right now."
One conservative Senate Republican, Senator Rand Paul of Kentucky, told ABC's "This Week" that he was not opposed to renewing the benefit. He added: "I'm opposed to having it without paying for it."
With an extension of benefits costing $6 billion for three months, Democrats fear that paying for the program would mean cuts to other domestic programs that already have been under the budget knife.
Paul, like House Speaker John Boehner, the top U.S. Republican, also said that any extension should be coupled with new moves to create jobs.
As Obama nears the sixth year of his presidency, he has said he wants to step up efforts to help the needy. But his appeals drew fire from Republicans, who see them as attempts to increase taxes, particularly on the rich.
Republicans argue that the best way to spread the wealth is to create more of it by easing federal regulations and taxes.
MORE GRIDLOCK?
The new year raises a new question: Will Congress be more productive and popular in 2014 than in 2013 when it did not do much of anything and had an approval rating below 10 percent.
Despite a bipartisan budget deal at the end of last year, Congress is likely to remain a tough place to find common ground.
That is largely because lawmakers will be busy jockeying for position in advance of the November elections, when a third of the 100-member Senate and the entire 435-member House will be up for grabs.
"I don't see a lot coming from Congress," said Greg Valliere of The Potomac Research Group, a private firm that tracks Washington for investors.
"But I also don't see Congress creating any more debilitating crises, like another government shutdown," Valliere said.
"Republicans want to keep the focus on bashing Obamacare," the president's troubled healthcare program, Valliere said. "That's what they figure will do them the most good" in elections.
Republicans have been reluctant to extend long-term jobless benefits, arguing that the U.S. economy, with the jobless rate now at a five-year low of 7 percent, is on the mend and that such emergency federal assistance is no longer necessary.
Meanwhile, polls show most Americans support an increase in the minimum wage.
Republicans oppose an increase, contending it would do more harm than good by eliminating jobs and hurting businesses, particularly small ones.
"A minimum wage increase is good politics but bad economics," said Republican Senator Jeff Flake of Arizona.
Terry O'Neill, president of the National Organization for Women, a liberal advocacy group, has made winning a minimum wage increase a priority.
O'Neill cited federal statistics showing that from 2009 to 2012, the average income for the wealthiest 1 percent of Americans soared 30 percent. During the same period, the average income for the other 99 percent of Americans rose 0.4 percent.
"This must change," said O'Neill, whose organization is targeting for defeat in the November election any lawmaker who opposes an increase in the minimum wage.
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