WASHTINGON (CNN) -- A $6.4 billion plan to extend unemployment insurance benefits to eligible workers for another three months cleared a key procedural hurdle in the Senate on Tuesday as 60 senators -- including six Republicans -- voted to move ahead with debate on the measure.
"Today brought us a glimmer of hope," said Sen. Charles Schumer, D-New York, after the vote. "It shows that the big plates -- the tectonic plates in our politics -- are moving."
But House Speaker John Boehner said he told President Barack Obama a month ago that another extension of temporary emergency unemployment benefits "should not only be paid for but include something to help put people back to work. To date, the president has offered no such plan. If he does, I'll be happy to discuss it, but right now the House is going to remain focused on growing the economy and giving America's unemployed the independence that only comes from finding a good job."
Still, the 60-yea votes were the minimum needed to allow debate to go forward and avoid a filibuster in the Senate. Democrats got help from Republicans Kelly Ayotte of New Hampshire; Dan Coats of Indiana; Susan Collins of Maine; Dean Heller of Nevada, Lisa Murkowski of Arkansas; and Rob Portman of Ohio.
The bill is a top priority for Democrats, but most Republicans object to it, with many arguing that the costs of extending the benefits need to be offset with spending cuts elsewhere in the federal budget.
Senate Democrats scrambled to clear the procedural hurdle to move forward on extending long-term unemployment benefits to 1.3 million Americans who lost them after the Christmas holiday.
With more than a dozen lawmakers absent due to weather-related travel delays, the Senate had postponed the key procedural vote from Monday.
Extending benefits is a priority for congressional Democrats and President Barack Obama, who is trying to make income equality a centerpiece of his second term. Obama contacted several GOP senators to persuade them to support the bill.
The White House Office of Management and Budget released a statement Monday urging Congress to pass the measure. Obama was to make a speech later Tuesday morning calling for passage of the bill.
Many Republicans argue the extension would hurt the economy and act as a disincentive to job creation. Others members of the GOP have signaled they might back an extension if the cost is offset by budget cuts elsewhere.
Sen. Mark Kirk of Illinois said he wants to help people, but insisted Congress must find a way to pay for the measure.
"I, obviously, have people in my state who would benefit. The better way to go is to not add to the deficit in an irresponsible way," Kirk said.
"I want us to get on the bill so we can talk about an offset to pay for it," said Collins of Maine. "Ultimately, I think we should restructure the unemployment compensation program so it's more closely linked to job training for the long-term unemployed whose jobs probably are not coming back."
Seventeen senators absent
In remarks just before the vote was to have been held Monday, Sen. John Cornyn of Texas, the No. 2 Republican in the Senate, noted the absence from the chamber of 17 members and urged that the proceedings be delayed "so we can have a real debate" and decide how to pay for the extension.
Winter weather that plunged the Midwest and much of the South into a deep freeze has triggered widespread travel delays.
Sen. Lindsey Graham, a Republican, tweeted that his commuter flight bound for Washington returned to South Carolina shortly after takeoff due to a possible engine problem and made a safe emergency landing.
Benefits for the long-term unemployed expired last month after Congress opted not to continue a 2008 recession-era law providing nearly a year of payments, footed by U.S. taxpayers, that kicked in when state jobless benefits ran out.
Democrats insist the program is critical to help Americans who are struggling and to maintain the economic recovery.
Republicans argue that the program -- which the Congressional Budget Office estimates would cost $26 billion to continue for another year -- is costly and is a disincentive to looking for work.
The U.S. unemployment rate stood at 7% in November, the most recent Labor Department statistics show. That means more than 10 million people were out of work, a third of them for at least 27 weeks.
Over the weekend, key Republicans, including potential 2016 presidential candidate Sen. Rand Paul of Kentucky, insisted that an extension must include cuts elsewhere to offset the cost.
"I'm opposed to having it without paying for it," Paul told ABC's "This Week." "I think it's wrong to borrow money from China or simply print up money for it."
Boehner will insist on such offsets before agreeing to an extension, a spokesman for the Republican leader said.
Obama supports passage
Conservative interests were applying heavy pressure.
The Club for Growth had urged all senators to vote "no" on the proposal and cited the lack of spending offsets.
"Congress should end the federal unemployment insurance program and return the authority back to the states, which already have programs in place," the group said.
"Absent this, Congress should pay for this extension by cutting spending elsewhere in the budget. After six years, an extension can no longer be called an 'emergency' with any credibility. There is plenty of waste in the federal budget from which to find an offset," it said.
CNN's Alan Silverleib contributed to this report.