Image caption The protesters say the Republican-backed anti-union bill threatens their livelihood

Thousands of union members and supporters have amassed in Wisconsin for a fourth day to keep up the pressure on a Republican-backed bill that would curb union rights.

Public sector workers and supporters crowded into the state capitol.

The bill would restrict some workers' collective bargaining rights and raise worker contributions.

Democrats in the state Senate have fled the city of Madison to deny the body a quorum for a vote on the bill.

National significance

Opponents describe the bill, which would also dramatically increase the amount public workers must contribute to their pensions and health insurance coverage, as an attack on livelihoods and on the unions.

It would still allow public workers to organise into unions, but they could not require workers to pay dues and would have to hold a vote annually to remain organised.

Also, the workers would be forbidden to bargain collectively on any matter except pay increases that are no higher than inflation.

Wisconsin Republicans' effort to trim public employee compensation is part of a nation-wide movement for the party, which made sweeping gains in the November election in part amid pledges to cut government spending, analysts say.

The state faces a $3.6bn (£2.23bn) budget deficit in the coming two-year period. The public employee bill is expected to save $300m in that period, and Governor Scott Walker says that despite the protests, he has the backing of the state's voters.

And he has said the bill is necessary to avoid painful job cuts.

This week, national political figures waded into the Wisconsin budget battle.

President Barack Obama described the bill as "an assault on unions" during an interview with a Milwaukee, Wisconsin television station.

Richard Trumka, president of AFL-CIO, one of America's largest unions, told the cheering crowd on Friday the Republicans were "on the wrong side of history" and said the bill was an attack on the middle class.

"You're standing in the doorway of our country's most basic values and cherished aspirations," he said, addressing Mr Walker. "Governor Walker, you're asking too much. We won't give it to you and you can't take it away from us."

Civil rights leader Jesse Jackson told the crowd they were fighting for a just cause and likened the protest movement to the pro-democracy uprisings in Egypt and Tunisia.

And across Wisconsin, school were shut because teachers were absent protesting in the capitol.

The legislation had been expected to pass the Republican-led Wisconsin state legislature on Thursday, with Mr Walker and Republicans arguing they had the voters' backing.

But Wisconsin Senate rules require 20 senators to be present for a quorum; Republicans hold 19 seats and the Democrats 14. Senate Democrats did not show up for the session, and aides told reporters they did not know where the legislators had gone.

The Republican senate leadership despatched state troopers to the home of Democratic senate minority leader Mark Miller in an effort to bring him to the capitol for a vote.

But in a series of interviews from the neighbouring state of Illinois and on the telephone, the Democratic senators threatened to remain in hiding for weeks, a move that would paralyse the state government.

Image caption With teachers protesting, dozens of Wisconsin schools were closed

Democratic Senator Jon Erpenbach said Democrats had left to slow down the bill in the hope of forcing Republican Governor Scott Walker and Republican legislators to negotiate.

"What we're trying to do is get the governor to sit down and at least try to talk with people who have some issues with what he's trying to do," said Mr Erpenbach told a Wisconsin radio station over the telephone from Chicago.

"This isn't about the money. This is all about the collective bargaining rights that the governor wants to take away from the unions."

Mr Walker, meanwhile, called on the Democrats to return.

"The state senators who are hiding out down in Illinois should show up for work, have their say, have their vote, add their amendments," he told CBS news on Friday, "but in the end, we've got a $3.6bn (£2.23bn) budget deficit we've got to balance."