Madison, Wisconsin (CNN) -- A left-leaning website that union supporters used to rally protesters in Wisconsin was partially blocked as demonstrators gathered in the state Capitol over a controversial budget bill.

The website, defendwisconsin.org, could not be accessed on Monday and into Tuesday morning in the Capitol building, where crowds assembled over proposed legislation that would increase the costs of benefits to public employees and curb their collective-bargaining rights.

Wisconsin Democratic Party press secretary Graeme Zielinski blamed Gov. Scott Walker and Republican lawmakers -- who returned to work Tuesday -- for causing the outage.

"In a direct assault on the First Amendment, Scott Walker's administration is blocking access in the Wisconsin Capitol to opposition websites," Zielinski said.

The governor's spokesman, Cullen Werwie, responded Tuesday, calling the accusation "a lie."

"The Department of Administration blocks all new websites shortly after they are created, until they go through a software approval program that unblocks them," Werwie said. "Within 30 minutes of being notified this website was blocked, DOA circumvented the software and immediately made the website accessible."

He said, "The Democratic Party should spend less time lying about Gov. Walker and more time trying to get their AWOL state senators back to Wisconsin," referring to Democratic efforts to prevent a quorum in the Senate.

The Capitol internet service, which restricts access to certain websites considered inappropriate for lawmakers, revealed a "blocked page" when users tried to access the site using the building's wireless system.

Users were able to access the site elsewhere.

The outage comes on the heels of a speech by Walker, who defended the budget proposal and criticized unions for squandering state coffers and impeding fiscal reform.

"We're broke," he told reporters Monday. "You really can't negotiate when you don't have money to negotiate with."

Unions have argued that collective bargaining -- a process of negotiations meant to regulate working conditions -- has helped protect wages and health care, enforce workplace safety and serve as a means to arbitrate employee grievances.

The budget-repair bill, proposed by Walker to address a $137 million shortfall through June 30, would increase contributions of state workers to their pensions and health insurance benefits. It requires collective-bargaining units to conduct annual votes to maintain certification. It also eliminates the right of unions to have dues deducted from worker paychecks.

Walker warned that not passing the proposed bill would result in at least 1,500 government employees being laid off in the short term and could result in the layoffs of upward of 6,000 workers in the following budget cycle.

Last week, 14 Democratic state senators essentially boycotted the Legislature and went to Illinois to prevent a quorum from passing the bill. The measure's opponents said they won't allow a vote unless Walker negotiates on the plan to eliminate collective-bargaining rights for everything but wages.

CNN's Chris Welch contributed to this report.