SÃO PAULO—Brazil’s deepening political crisis moves dramatically—and some believe decisively—into the streets on Sunday after playing out for months in congressional halls and judges’ chambers with no clear resolution.

Massive antigovernment demonstrations are planned in more than 400 cities, capping a hectic week in which prosecutors moved to arrest former president Luiz Inácio Lula da Silva, Brazil’s most popular and controversial politician, on money-laundering charges.

That action further polarized Brazil’s tense and angry citizenry, setting the stage for what many think could be a pivotal weekend showdown over whether Dilma Rousseff, Brazil’s embattled president and a protégée of Mr. da Silva, stays or goes.

Matthew Taylor, an associate professor at American University, said the scale of the demonstrations could sway opposition political leaders who are threatening to impeach Ms. Rousseff.

“The Sunday protests, if they are nationwide, will in many ways put spine in the opposition or take the spine out of the opposition,” Mr. Taylor said.