The cloture vote that passed 60-40 this afternoon provides for up to 30 hours of debate that Republicans could yield back, allowing a vote much sooner on the legislation.
"We only need a simple majority to pass this bill now, but they're making us wait," Reid said. "I just can't articulate in strong enough feelings how unfair this is to 2.5 million people."
The House Rules Committee provided an avenue for the bill to be considered quickly on Wednesday once the Senate completes the measure.
The Senate could vote on the measure as late as 9 p.m. Wednesday -- at the end of the 30 hours -- then send the bill to the House.
Reid said he hoped that an agreement could be reached with Republicans to take up the bill earlier in the day. He said once the bill is completed the Senate will resume consideration of the small business jobs bill.
After today's vote, Senate Republicans continued to insist that the bill could've been paid for with stimulus funds or other spending cuts.
"I don't know anybody who's not in favor of extending unemployment, but I will remind you that the president just last November, when we did a previous extension of unemployment insurance, that it was done in a responsible way and it was paid for," Senate Minority Leader Mitch McConnell (R-Ky.) said Tuesday.
One Democrat -- Sen. Ben Nelson of Nebraska -- continued his opposition to the bill.
"I oppose another $33 billion in deficit spending and increasing the debt," he said. "The six-month extension of unemployment benefits is a priority that can and should be funded. Some of the $70 billion in offsets included in earlier proposals could have been used to offset the $33 billion in new spending in this bill."
President Obama is expected to sign the bill before the week's end.
The bill will provide retroactive benefits to June 2 and run through November 30.