Senate Majority Leader Harry Reid, the top Democrat in Congress, practically dared Senate Republicans on Sunday to try to block a measure to extend unemployment insurance for the longtime jobless.

"It would seem to me that five Republicans in the Senate should agree with the Republicans around the country," Reid said on CBS's "Face The Nation," citing broad public support for extending unemployment insurance. "Republicans around America want us to do something to extend these benefits. Why? Because it's good for the economy."

Congress allowed insurance beyond 26 weeks of unemployment to expire at the end of the year, eliminating 1.3 million people from receiving government aid. Should it not be extended, as many as 1.9 million more people could lose their benefits in the first half of this year.

President Obama and Democrats have vowed to take up the political fight over unemployment insurance again in the first few months of 2014, and the Senate is expected to vote this week on a measure to extend benefits.

To do so, however, Reid and Democrats will need to persuade at least four more Republicans to back the measure to avert a filibuster. One Republican, Sen. Dean Heller, R-Nev., has already expressed his support.

Another high-profile filibuster could compound Democrats' frustration with Republicans' use of the tactic in the Senate, and Reid hinted Sunday that he might in the future consider further limits to the filibuster, which he pared back last year.

"Would you do away with filibusters entirely?" the show's host, Bob Schieffer, asked Reid.

"We're not there yet. ... I'm not thinking about that today," Reid said. But, he added, "Everyone should understand that the country cannot continue on the road that it's on."

Should the Senate approve an extension, House Republicans still likely will not be eager to extend unemployment insurance, which would come with a price tag of $26 billion for one year.