Prime Minister Benjamin Netanyahu planned to sign agreements on Thursday to form a government with Yair Lapid and Naftali Bennett, two dynamic, first-time politicians who represent vastly different constituencies but teamed up to turn Israel’s coalition negotiations into a bitter six-week struggle of slights and squabbles.

The new coalition will include 68 of Parliament’s 120 members, from five factions, and be led by 21 ministers, down from 30 in Mr. Netanyahu’s previous government. It excludes the ultra-Orthodox parties for only the third time since 1977, leaving a mix of right-wing nationalists and center-leftists.

And most analysts see it as a weak, fragmented group that will have trouble tackling the toughest issues: the coalition agreement calls for a return to negotiations with the Palestinians, for example, but the housing minister is a former chief of the settlers’ council, whose plan to expand Jewish communities in the West Bank is anathema to the two-state solution advocated by Tzipi Livni, who has been tapped to lead a renewed peace process.

“Essentially, the question is: Will this baby, which was born of rape, be able to function?” asked Nahum Barnea, a prominent columnist, in Thursday’s Yediot Aharanot newspaper. Writing in the same paper, Yoaz Hendel said, “It has been many years since there has been a government with such a high potential for producing change and such a high potential for falling apart.”

Gil Hoffman, The Jerusalem Post’s political reporter, said that when President Obama arrives in Israel on Wednesday, he “will find a Netanyahu who has been weakened by an election that disappointed him and a coalition-building process that left him much less powerful.”

“The man crowned King Bibi by Time magazine just nine months ago,” Mr. Hoffman wrote, using Mr. Netanyahu’s nickname, “will now have to consult with Prince Yair on the left and Duke Naftali on the right when making key decisions.”

Ultra-Orthodox leaders and others left out of the coalition vowed to form a vigorous opposition, predicting class warfare and denouncing the government as a bourgeois one dominated by settlers and “tycoons.”

“All those that belong whose common denominator is that they belong to the have-nots, to the second Israel, all these will fight shoulder to shoulder until the class gap ceases to exist,” Aryeh Deri, a leader of the ultra-Orthodox Shas faction, wrote on his Facebook page. “Gone are the days in which there is a coalition and opposite there is a weak opposition whose voice is not heard.”

Dov Hanin, a Parliament member from the far-left Hadash Party, called the new government “dangerous,” and Zehava Galon of the left-leaning Meretz said the “extreme right and its settlement enterprise” were the big winners. Isaac Herzog of the Labor Party, the largest in the opposition, declared, “We intend to fight about everything.”

“We will present alternatives about every single subject,” Mr. Herzog said in a radio interview, predicting that the makeup of the coalition would “bring about a complete paralysis in the peace process.”

Mr. Lapid, the former television broadcaster whose centrist, mostly secular Yesh Atid party shocked the world by winning 19 seats in the Jan. 22 election with a focus on domestic concerns and a promise of new politics, emerged with several critical accomplishments.

He not only prevented the ultra-Orthodox from joining the coalition but won vows to end the widespread draft exemptions for yeshiva students and to overhaul the curriculum of religious schools to include more math, English and science. In the final hours of negotiations, he wrested the education ministry for his party’s No. 2, a modern Orthodox rabbi. And he kept the cabinet small, if not quite as small as he had hoped.

Mr. Lapid himself will serve as finance minister, a post with the potential to deliver on the economic campaign promises of his party, whose name means There is a Future, though also fraught given Israel’s gaping $10 billion budget deficit.

“Lapid’s victory is absolute and cannot be explained away by punditry,” wrote Sima Kadmon, another Yediot columnist. “He didn’t appear desperate because he wasn’t. He didn’t appear eager because he really didn’t feel eager. Netanyahu senses that, exactly the way a man senses when a woman doesn’t really want him.”

Mr. Bennett, whose revitalized Jewish Home party represents the so-called religious Zionists and attracted many settlers with his plan to annex a large area of the West Bank, grew in stature through the negotiations, particularly by brokering the final deal as the deadline for forming a government — and Mr. Obama’s visit — approached. In addition to the Housing Ministry, his 12-seat faction will control Parliament’s powerful finance committee. And while Mr. Bennett himself will be economics and trade minister, not the highest-profile of jobs, he also secured control over religious services, diaspora affairs and Jerusalem.

Moshe Yaalon, a former chief of Israel’s military and member of Mr. Netanyahu’s Likud Party, will become defense minister. The Foreign Ministry, which Mr. Lapid originally coveted, is being held for Avigdor Lieberman, the leader of the Yisrael Beiteinu faction that joined with the Likud for the election campaign. Mr. Lieberman resigned the post in December after being indicted on a charge of fraud but hopes to return to it once his trial is concluded. Ms. Livni, a former foreign minister whose new Hatnua Party has six Parliament seats, will be justice minister, with a special portfolio dealing with the peace process.

Speaking to members of the combined Likud-Beiteinu group at the Parliament building on Thursday, Mr. Netanyahu described the defense and foreign ministries as the most important, and suggested he would soon return the public focus to the Iranian nuclear threat and other security matters that are his forte.

“We kept power,” Mr. Netanyahu cited as his main accomplishment. “This term will be one of the most challenged in Israel’s history,” he said. “There is a gap between the challenges and threats before us and the public attention to this, but we have no gap.”

Writing in the Israeli daily Maariv, Shalom Yerushalmi said the new government “will in fact be two governments” — one of foreign policy, led by Mr. Netanyahu and Mr. Lieberman, and one social-economic, led by Mr. Lapid and Mr. Bennett, whom Mr. Yerushalmi called “the big winners.”

Yossi Klein Halevi, an author and senior fellow at the Shalom Hartman Institute, said that the unusually contentious coalition negotiations had been “thrilling” for an Israeli public that had used its Jan. 22 ballot to demand an overhaul of the political system.

“In the past all the coalition negotiations were about one issue, cabinet positions,” Mr. Halevi said in an interview. “The new guys in town changed the rules. They’ve made the negotiations about principles.”

“This is an extraordinary moment for Israel,” he added. “On the one hand, our security situation is becoming increasingly desperate, but on the other hand, the political system is for the first time in decades focused on a domestic agenda. This is Netanyahu’s great failure, because Netanyahu is all about the security agenda, and other parties have stolen the country’s agenda from him.”