Mr. Netanyahu quickly grasped the significance of the protests and, canceling a trip abroad, issued directives and plans to ease the burden on consumers. He has proposed new rules to make housing more affordable and has frozen gasoline prices, while his public responses have been dominated by bold talk of ending monopolies and sympathy for the demonstrators. On Sunday, the director general of the finance minister resigned as a result of the protests.

But Mr. Netanyahu may not have sidestepped the political risk. One of the most debated questions is whether the movement is creating an opening for the country’s battered and dormant political left to challenge his leadership. Many think the answer is yes but only if it stays focused on social and economic issues and avoids the geopolitical and security ones where its views are in the minority.

Last week, the powerful Histadrut labor federation announced its strong support for the protests.

“The left has risen back to life,” Shai Golden, deputy editor of the newspaper Maariv, said in a column on Sunday. “It hasn’t yet dared to let the words ‘occupation’ and ‘settlements’ cross its lips and to cite the social and economic price that they have cost Israel over the course of the past four decades.” The new movement, he added, would be “the social left.”

Two decades ago, when Yitzhak Rabin defeated Yitzhak Shamir for prime minister, ending 15 years of domination by the conservative Likud Party, Mr. Rabin spoke of the need “to change the national order of priorities and the allocation of financial resources.” He largely froze settlement building in the West Bank and Gaza and said he was redirecting resources to the towns in the Israeli Negev and Galilee.

The left today hopes to revive itself with similar plans. The mayor of Beersheba, Ruvik Danilovich, who is an independent with roots in Labor, said in an interview in Maariv on Sunday that the theme of the new movement is “social justice, meaning a change in priorities.” He listed education, health care and affordable housing. He added of the Saturday night protest, “This was a landmark event. The norms that have been accepted in the past will not be in the future.”

The left hopes that in the coming year or two it could sweep back to power through a focus on social issues and then, in the bargain, shift the country’s external policy. The left would heavily curtail settlement building in the West Bank and has shown greater willingness to yield territory to the Palestinians and to share Jerusalem in a two-state solution.