By James Kelleher

MADISON, Wisconsin (Reuters) - Wisconsin Senate Republicans sent police on Thursday to find at least one of the 14 runaway Democrats who fled the state to block a vote on a spending bill that would curtail public union bargaining rights.

Republicans sent state patrol officers to the homes of the Democrats in a failed attempt to break a standoff that has blocked Republican Governor Scott Walker's proposal to strip most collective bargaining rights from public union workers.

All 14 Democrats in the Senate fled to Illinois last week to deny Republicans a quorum and a vote on the bill, which has become a flashpoint in a growing national struggle over labor union power.

Republicans hold a 19-14 majority but need a quorum of 20 to vote on spending bills. The Democrats fled the state out of fear they could be compelled to attend a quorum call if they remained.

Some Republicans believe the Democrats have been sleeping in their own beds at night. Republican Senate Majority Leader Scott Fitzgerald said he hoped the Democrats could be convinced to return, although he acknowledged the officers cannot arrest them.

"It's a gesture that shows we're still serious and a call of the house should be honored," Fitzgerald told the website Wispolitics.com.

The move came as Democrats and Republicans in the lower house of the state legislature, the Assembly, agreed to limit debate and vote later on Thursday on the bill, which Walker says is necessary to close a budget deficit of $137 million for this fiscal year.

The agreement came after a second straight all-night session in the state Capitol, about 43 hours after the Assembly took up the proposal on Tuesday.

But approval in the assembly, where Republicans hold a 57-38 majority, will not ease the Senate standoff over a plan that has generated widespread protests among Wisconsin teachers and other union members.

More than 50,000 demonstrators poured into the state capital of Madison over the weekend to protest against the plan. If Republicans prevail in Wisconsin, several other states could be inspired to take on the powerful public unions.

U.S. state and local governments are struggling to balance budgets after the recession decimated their finances. Other states like Texas, Arizona and Ohio are relying mainly on cuts in spending, while Minnesota and Illinois are raising taxes.

In Indiana, Democrats boycotting the state legislature appeared to score a victory on Wednesday when a "right to work" law that would restrict unions was put aside until next year.

The Wisconsin changes sought by Walker would make state workers contribute more to health insurance and pensions, end government collection of union dues, let workers opt out of unions and require unions to hold recertification votes every year. Collective bargaining would be allowed only on wage increases up to the rate of inflation.

The governor says the changes are needed to close a budget deficit of about $3 billion over the next several years.

But Democratic lawmakers and unionized public employees said the measure is an attempt to bust the unions and choke off funding to organized labor, the single largest source of funding to the Democratic Party.

Walker wants the bill passed by Friday as part of a plan to push principal payments on general obligation bonds into future years to save $165 million. Under that plan, the bill must be passed by Friday to allow time to sell the debt.

(Reporting by James Kelleher and Jeff Mayers. Editing by Peter Bohan and John Whitesides)