MADISON, WIS. - Tens of thousands of demonstrators swarmed the state Capitol building here Saturday in protest of Gov. Scott Walker's proposal to strip public employees of most of their collective bargaining rights.

Protesters have crowded around the Capitol for more than a week, since unrest erupted over the Republican governor's plan. Local media quoted police as saying the crowds Saturday were on track to rival those last weekend, which were estimated at nearly 70,000. Walker threatened on Friday to trigger as many as 12,000 layoffs beginning next week unless lawmakers enact his plan.

The demonstration is certain to be the largest of dozens taking place around the country against Walker and other Republican governors who have taken similar stands against their public employee unions. The progressive group MoveOn.org said it would hold "Save the American Dream" rallies in all 50 states, including one that drew hundreds of people to Dupont Circle in the District on Saturday afternoon.

Although unions have offered concessions they say would close the state's budget gap, Walker remained determined to achieve a resolution that he said would give state and local governments leverage to limit employee costs well into the future.

Without legislation to pare back employee health-care and pension benefits while repealing most collective bargaining rights for many public employees, Walker said, he would be forced to make cuts elsewhere in the budget that could lead to massive numbers of state and local employees losing their jobs.

"If we want to avoid the layoffs that will eventually come at the state and local level, the only way to achieve that" is to pass the bill, Walker said.

The layoffs would mark an escalation of a battle that has paralyzed the state Capitol. Fourteen Democratic state senators have fled Wisconsin to prevent the state Senate from having a quorum for considering the measure. Walker backed off earlier remarks that the layoffs would begin this week.

Nationally, Walker's efforts to break the power of public service unions - being replicated to some degree in several other Republican-led states - have thrown public employee unions into an existential crisis.

As a group, public employees generally earn less than comparably educated private-sector employees, but they tend to enjoy far better health-care and retirement benefits. The issue of their compensation has gained particular resonance at a time when states and municipalities across the country are struggling with huge budget deficits and ballooning costs for employees' health-care and pension obligations.

The controversy has lifted Walker to national prominence, and he says he is determined to make Wisconsin a leader in remaking the way state and local governments deal with their employees.

The clashes over public employee unions continued in other state capitals. In Indianapolis, hundreds of union supporters demonstrated at an otherwise quiet statehouse Friday as there appeared to be no end in sight to a partisan standoff that has paralyzed the legislature.

"I'm here to help save the jobs of thousands of hardworking Hoosiers," said Jim Szucs, a Teamster from South Bend, Ind.