WASHINGTON (Reuters) - A measure that would restore lapsed jobless aid for hundreds of thousands of Americans cleared a hurdle in the U.S. Senate on Wednesday, clearing the way for passage later in the week.

By a vote of 60 to 40, Democrats voted to set aside a law that requires new spending to be offset with tax increases or spending cuts elsewhere.

Democrats had fallen short of the 60 votes needed for passage earlier in the day, when Vermont Senator Patrick Leahy was at a funeral.

With the unemployment rate at 9.7 percent, some 6.1 million Americans rely on jobless benefits to help them pay the bills as they look for work as the United States climbs out of the worst economic downturn in 70 years.

Those benefits expired for more than 200,000 Americans last week after Republican Senator Tom Coburn prevented a vote at the end of March, shortly before Congress left on a two-week break.

Another 200,000 Americans will lose their benefits this week if Congress does not renew them, according to the National Employment Law Project, a liberal advocacy group.

Coburn and other Republicans argue that Congress should find a way to pay for the $9.2 billion cost of extending benefits, rather than letting it add to a budget deficit projected to hit a record $1.5 trillion this fiscal year.

Wednesday’s vote was the second procedural roadblock thrown up by Republicans in a process that could take most of the week. One Republican, George Voinovich of Ohio, from the economically struggling state of Ohio, voted with Democrats.

Democrats say jobless aid has always been considered emergency spending during times of high unemployment and thus does not need to be offset.

They say Republicans are blocking an extension because they have not decided to cooperate on anything.

“We have groups of senators on the other side deciding they’re going to dig in their heels and prevent anything from happening,” Democratic Senator Byron Dorgan said at a news conference.

Jobless benefits normally expire after six months but Congress has extended the program several times during a slump marked by record levels of long-term joblessness.

Democrats have been extending the program on a month-to-month basis as they work on a longer-term fix.

Along with the difficulty faced by the jobless who have benefits, the standoff has also disrupted a federal flood-insurance program, which has held up roughly 1,400 home sales each day in flood-prone areas, and slashed emergency loans to small businesses, Democrats said.

COBRA health-insurance subsidies for the unemployed and payments to doctors under the Medicare health program have also been disrupted.

Democratic leaders have promised that these programs will be reinstated retroactively.