Three young Palestinian women sat on the floor at a summer camp this week surrounded by Legos and 3-year-olds. As the toddlers played, the women taught them the color of each block, repeating the words in Arabic, azrak for blue or akhdar for green.

But the seemingly simple scene here in the Galilee was actually caught up in some of the most contentious issues confronting Israeli society: How do Arabs reconcile their identity as citizens of a Jewish state? What is the appropriate role for a growing Arab minority in a state determined to be democratic and Jewish?

The  young women are volunteers in Israel’s national service program, an alternative to the military that comes with the same financial benefits and similar advantages for future education and employment. That program is now the focus of a searing national debate over plans to draw up a law that will no longer exempt categories of citizens. Some Arab-Israeli leaders see the young women’s service as a betrayal of their national struggle, and call them traitors.

“I will not deny or forget my identity,” said one of the counselors, Nagham Ma’abuk, 19, who grew up in Nazareth, a northern city known as the Arab capital of Israel. “But this can help me in the future. We need to live together in coexistence. You can’t determine equality according to what’s convenient for you.”

With a looming Aug. 1 deadline to rewrite a law invalidated by the Supreme Court that exempted thousands of yeshiva students from the draft, Israel’s government and populace have been in turmoil for weeks over how to integrate the country’s minority populations into the military and civilian service programs.

While most of the attention has been focused on how many ultra-Orthodox men should be drafted, the parallel issue of Arab service has revived the raw, decades-old conundrum of what it means to be both Arab and Israeli — citizens of a state whose defining philosophy most find alienating at best, often considered enemies within, with a list of complaints about discrimination in employment, education and housing.

This state of affairs cannot continue, some argue. “The 1948 paradigm is collapsing,” said Elie Rekhess, a historian of Arab-Jewish relations who retired from Tel Aviv University and is now co-chairman of the Middle East Forum at Northwestern University. “It’s not that every Arab wakes up in the morning and says, ‘Oh, which part of the hyphenated identity will I be identifying with today?’ But as far as leadership is concerned, they are challenged by the contradictions and the impossibility of this situation of being Arabs in a Jewish state.”

When modern Israel was created 64 years ago, its Declaration of Independence promised “complete equality of social and political rights to all its inhabitants,” and in 1952 citizenship was granted to about 150,000 Palestinians living within its borders. Today, 1.6 million Arabs live in Israel, making up about 20 percent of the population, with an average income less than two-thirds that of Jewish residents, according to statistics compiled by Professor Rekhess, and a poverty rate nearly three times as high.

The conundrum over national service is hardly the first such identity crisis. Many Arab citizens observe Israel’s Independence Day by mourning what they call the Naqba — the catastrophe. They attend separate schools, where last month many protested a new curriculum focusing on Menachem Begin and David Ben-Gurion. Even the nomenclature has caused disputes: After decades of calling themselves Israeli Arabs, which in Hebrew sounds like Arabs who belong to Israel, most now prefer Palestinian citizens of Israel.

A dozen of Parliament’s 120 members are Arab. So is one of the 15 Supreme Court justices. His recent refusal to sing the national anthem, which refers to the “yearning of the Jewish soul,” caused much soul-searching. When a Bedouin professor was chosen last month as the first non-Jewish president of a college, some on campus questioned how he could uphold its tradition of contributions to the state.

Ehab Helo, a 25-year-old architecture student, confronted a personal version of the problem two years ago when he designed a minimalist chair that won a student contest, but refused to compete internationally under the Israeli flag with its Star of David.

“I said to them, ‘This is the Jewish flag, not the Israeli flag,’ ” Mr. Helo recalled as he sat at a cafe on Ben-Gurion Street in Haifa. “I am angry that I didn’t have the opportunity to be in Italy in a bigger competition; I’m also happy that I said no to be who I am.”

The current focus is on national service, with a proposal expected to be submitted to the cabinet by Sunday that includes a goal of doubling by 2016 the 2,400 Arabs now participating — still a small fraction of the 30,000 eligible each year. (Palestinians have never been required to serve in Israel’s military, though about 250 were enlisted last year. The Druse, another Arab minority, are subject to the draft, while the Bedouin, who are also exempt, tend to join in greater numbers.)

Many who support expanding or even requiring service by Arabs note that about three-quarters of current Arab volunteers serve in Arab community institutions like the Nazareth summer camp. Like soldiers, they receive small monthly stipends and a lump sum upon completion that can be used for education, weddings, mortgages or business development.

Prof. Sammy Smooha of Haifa University, who has studied the issue for years, said support for national service had dropped among Palestinian citizens, even as participation had increased tenfold since 2005-6. Forty percent of Arab youths said last year that they would be willing to serve, down from 53 percent in 2009, and 62 percent of the Arab public backed the program, down from 78 percent in 2007.

“You have to compare it with blacks in the U.S. during World War II,” Professor Smooha said. “Why did they want to serve? Because they identified themselves with the state and they saw this as a vehicle to change their status. The Arab leaders do not see it this way. They see it as a means of repression of Arabs in Israel.”

A leading Arab community group recently had a poster contest opposing the program. Entries included a large soiled foot captioned, “National Service: A Dirty Business,” and a headless woman in an Army uniform over the slogan, “Civilian Service: The Way to Erase Identity.”

Hanin Zoabi, a Parliament member from Nazareth, called the proposal to expand service “a trap.”

“In order for us to get our natural right, we have to be loyal to the country,” she said in an interview. “They are talking about dividing the burden. All the country’s burdens are on my back. Six million Jews are living on my land. We ask Israel to withdraw the definition of a Jewish state, and maybe then it will turn into a democratic country.”

In Wadi Nisnas, a Haifa neighborhood — where a sign for Hadad Street notes, in Hebrew, that it is home to Israel’s oldest Arab families — four teenagers training a makeshift summer camp marching band on Wednesday pronounced themselves “against, against, against and against” national service for Arabs.

“It’s against our people,” said Rozeen Kanboura, 18, who works at a McDonald’s. “We are betraying our homeland, our origins, our history.”

Ayan Abunasra, articulate beyond her 13 years, said, “I don’t feel part of this country.”

“Put yourself in our place,” she said. “You’re going to serve a country that occupied your land and your great-grandparents died because of it?”

Moments later, she and the others stood in front of two lines of children, 15 of them with red drums around their waists, one little girl holding a pink stuffed bunny. A Palestinian flag flew from an apartment overhead.

They are volunteers, just like Ms. Ma’abuk in Nazareth — only with no connection to the state, and none of its attendant pluses and minuses.