"It's the right thing to do. We have long-term unemployment. That's why the American people support this -- Democrats, Independents and Republicans," the Nevada senator said on CBS' "Face the Nation."
He said he is supporting a plan that would restart the benefits for three months before determining how to offset the cost of doing so.
The support of five Republicans is necessary to avoid a filibuster.
But many Republicans have spoken out against approving benefit checks without finding a way to pay for them.
Reid urged Republicans to follow the example of Sen. Dean Heller, R-Nev., who is co-sponsoring the bill.
"He's a guy who is really a conservative person and he wants to extend unemployment benefits. I admire him. Can't we get four Republicans to agree with the American people that we should do that? I would certainly hope so," he said.
Reid also spoke in favor of raising the minimum wage and said the agenda should focus on the middle class, not deficit reduction.
"We have a situation in America today that is really not good. ... the rich are getting richer, the poor are getting poorer. Middle class [families] are being squeezed out of existence," he said.
To combat the deficit, Reid suggested Republicans pass comprehensive immigration reform legislation that would save an estimated $200 billion in federal deficits over the next 10 years.