MADISON, Wis. >> Wisconsin state troopers were dispatched Thursday to the doorsteps of some of the AWOL Democratic senators in hopes of finding at least one who would come back to allow a vote on a measure to curb the power of public-employee unions.

The stepped-up tactic ordered by the Republican head of the Senate came amid reports that at least a few of the missing senators were returning home at night to pick up clothes, food and other necessities, before rejoining their colleagues in Illinois.

Meanwhile, the state Assembly appeared close to voting on the bill after more than two days of filibustering.

Democrats agreed before dawn Thursday to limit the remaining number of amendments they offer and the time they devote to each one. More than 12 hours after the agreement was announced, Republicans voted to cut of discussion on all amendments. Democrats then spent hours delaying a vote on the measure that Gov. Scott Walker insists is necessary to ease the state’s budget woes and avoid mass layoffs.

Democrats urged Republicans to accept a compromise that would keep collective bargaining intact.

“We all know there is an impasse. There is one person who can end this impasse and that is Gov. Walker,” said Democratic Assembly Leader Peter Barca as debate reached its 53rd hour. “This state has never been more divided in the last 25 years. … It’s the governor’s job to unify the state.”

But Republicans summarily rejected every Democratic amendment in the marathon session, which unfolded as grand political theater. Exhausted lawmakers limped around the chamber, rubbing their eyes and yawning as Wednesday dragged into Thursday.

Around midnight, Rep. Dean Kaufert, a Republican from Neenah, accused Democrats of putting on a show for the protesters. Democrats leaped up and started shouting.

“I’m sorry if democracy is a little inconvenient, and you had to stay up two nights in a row,” Pocan said. “Is this inconvenient? Hell, yeah, it’s inconvenient! But we’re going to be heard!”

Democrats, who are in the minority, don’t have the votes to stop the bill once the vote occurs.

But even after the bill passes the Assembly, it cannot become law until it also passes the Senate, where action has been stymied by the Democrats’ absence. At least one of them needs to be there in order for Republicans to take up the bill since the GOP is one seat short of having a quorum.

The Senate convened at 7 a.m. Thursday just long enough to take a roll call, which allows for the sergeant at arms staff to go to missing lawmakers’ homes with police.

Troopers went to multiple homes but left after finding no one home, said Sergeant at Arms Ted Blazel.

Wisconsin law does not allow police to arrest the lawmakers, but Republican Senate Majority Leader Scott Fitzgerald said he hoped the show of authority would pressure them to return. He would not say how many Democrats were being targeted, but said it was more than one.

“Every night we hear about some that are coming back home,” Fitzgerald said. Whether to send police out again is a day-by-day decision, he said.

Democratic Sen. Jon Erpenbach, who was in the Chicago area, said all 14 senators remained outside of Wisconsin and would not return until Walker was willing to compromise.

“It’s not so much the Democrats holding things up,” Erpenbach said. “It’s really a matter of Gov. Walker holding things up.”

Walker, in a Capitol news conference, praised the Assembly for moving toward a vote and renewed his call for Senate Democrats to come back.

“It’s still my belief in the end they’ll come home,” he said.

Walker repeated his warning that if the budget bill does not pass by Friday, the state will miss a deadline to refinance $165 million of debt and will be forced to start issuing layoff notices next week.

While Walker is trying to increase the pressure to act, the deadlines may not be quite as strict as he says.

The nonpartisan Legislative Fiscal Bureau said in a memo sent to lawmakers earlier this week that the debt refinancing could be pushed as late as Tuesday in order to achieve the savings Walker is seeking.

The governor is trying to balance a projected $137 million budget shortfall by July.

Based on a similar refinancing in 2004, about two weeks are needed after the bill becomes law to complete the refinancing, which means if the bill is adopted by the middle of next week, the state can still meet a March 16 deadline, the Fiscal Bureau said.

Walker has suggested the deadline is actually Friday in order to pressure lawmakers to act on the bill, which has drawn tens of thousands of protesters to the Capitol. The rallies reached a high of 68,000 people on Feb. 19 and hundreds have stayed overnight.

Fitzgerald said the real deadline is “up in the air.”

“Everything’s in place, it’s ready to go,” he said. “It just needs to be finalized.”

Walker also threatened to start sending layoff notices to up to 1,500 state workers next week if the bill isn’t passed, arguing he has no other choice to deal with the shortfall. He has not said who would be targeted.

School districts already have started sending out preliminary layoff notices in case they are needed later.

The battle over labor rights has been heating up across the country, as new Republican majorities tackle budget deficits in several states. The GOP efforts have sparked huge protests from unions and their supporters and led Democrats in Wisconsin and Indiana to flee their states to block major legislation.

Wisconsin’s measure would forbid most government workers from collectively bargaining for wage increases beyond the rate of inflation. It also would require public workers to pay more toward their pensions and health insurance. Police and firefighters would be exempt.

In Ohio, a similar proposal in a Senate committee drew thousands of protesters to the Statehouse, just as in Wisconsin.

Indiana Democrats successfully blocked a Republican bill that would have prohibited union membership from being a condition of employment by leaving the state Tuesday. They remained in Illinois in hopes of derailing other parts of Republican Gov. Mitch Daniels’ agenda, including restrictions on collective bargaining by teachers.