Israel, bound by an international refugees treaty it ardently promoted, doesn't seem to have that option, and the gap between rhetoric and reality threatens to send simmering social antagonisms boiling over into open conflict.
It has raised questions, relevant all over the developed world, about how much is owed to the impoverished migrants who manage to sneak in.
Over the past seven years, as many as 60,000 African migrants, most from Sudan and Eritrea, have slipped across Israel's border with Egypt, exploiting the lack of a physical barrier and widespread lawlessness in the Sinai Peninsula that has been one result of the fall last year of longtime Egyptian ruler Hosni Mubarak.
Israel is erecting a barrier along the roughly 200 kilometers (125 miles) of border. While this work drags on, the migrants continue to arrive at a rate of about 1,000 a month, ragged and penniless, with some reporting being raped, tortured and extorted by the Bedouins who smuggle them through.
Some migrants are fleeing repressive regimes. Others are simply looking for a better life in a richer country. How many fit into each of those categories is a matter of deep disagreement between officials and migrant advocates.
Some Israelis worry that their national identity as a Jewish state is being threatened by unauthorized African migrants, who now make up less than 1 percent of Israel's population.
"It's the crumbling of the Zionist dream," Interior Minister Eli Yishai warned on Thursday.
Officials claim the overwhelming majority of the migrants are not bona fide refugees escaping persecution and war, but economic migrants looking for jobs. Israeli leaders use terms like "infiltrators," ''cancer" and "national scourge" to describe them, setting an inflammatory tone.
After the first rape was reported earlier this month, Yishai declared nearly all migrants to be criminals and said they should all be jailed pending deportation.
Days later, Prime Minister Benjamin Netanyahu warned, "60,000 infiltrators are liable to become 600,000, and lead to the eradication of Israel as a Jewish and democratic state."
The issue of how to deal with them has also caused introspection about whether Israel, after a century of conflict with Arabs, has become a racist society.
"What disturbs me most is the racist atmosphere," social commentator Tom Segev said. "For several years now, Israel society has been moving in that direction, with all the anti-Arab motions in the parliament. ... I think that this society is very sick now."
Others deny that the pushback is racist, finding it unreasonable that their country of about 8 million should be expected to throw open its doors to unlimited numbers of migrants.
Israel cannot simply kick out the Africans, as some politicians would seem to suggest. As an enthusiastic backer of a 1951 U.N. treaty drafted to address the plight of World War II refugees, it has pledged not to expel asylum-seekers to any country where they would be in danger.
"We're not going to pull back on our obligations under the refugee convention," said Daniel Solomon, legal adviser to Israel's population and immigration authority. "At the same time, other solutions will have to be looked for," like finding a third country to take them in.
Because most migrants come from Sudan, an enemy state, and Eritrea, a country with an abysmal human rights record, the line between refugee and economic migrants is blurred. So Israel has quietly allowed most migrants from those two countries to stay, without processing their asylum applications.
This status does not allow them to work openly or access social services, so the migrants scrounge for whatever underpaid and insecure employment and volunteer health care they can find.
"Our objective is to have Israel host these people under proper conditions until the option arises for them to go home," said William Tall, the envoy of the U.N. refugee agency office in Israel.
The Africans began trickling into Israel after neighboring Egypt violently quashed a demonstration by a group of Sudanese refugees there in 2005, killing at least 20. The numbers surged as word spread of safety and jobs in Israel, a prosperous and liberal country reachable from Africa overland.
The swelling numbers have spawned slums. Fear and intolerance is mounting among locals, who accuse the migrants of stoking crime, including three recent rapes - even though police records show crime among the migrants is lower than among Israelis.
Firebombs were thrown recently at two buildings where migrants live, and a protest against them Wednesday in a poor southern Tel Aviv neighborhood where many Africans live turned violent. The crowd shattered windows of shops and cars belonging to Africans, police said, and a witness reported that protesters spat on migrants and cursed them. No one was hurt.
Bashir Abekker, 32, came to Israel four years ago to escape the war in Sudan's Darfur region. He thought he'd find safety, "but recently, I'm not safe here. I am afraid for my safety," he said. "After what happened (Wednesday), I was afraid to go out on the street to buy food."
On Thursday, Netanyahu condemned the violence. "I want to make it very clear that there is no room for the kinds of expressions and actions we saw last night," he said. "I say this both to public officials and to the residents of south Tel Aviv, whose pain I understand."
The Hotline for Migrant Workers advocacy group said the refugees are endangered by the "incitement" of politicians.
On the other side of the divide, neighborhood activist Dror Kahalani said the government is neglecting his already poor community to provide services for migrants, whose rising numbers terrify residents.
"I don't let my daughters go out unless I go with them," Kahalani said.
Prominent author and social commentator A.B. Yehoshua came to the defense of the migrants' Israeli neighbors. "We have to distinguish between economic migrants whom we don't have to accept, and the bona fide refugees who are suffering and face death if returned," he said.
For some, the violence against the migrants and calls for their expulsion are difficult to accept given the legacy of the Holocaust, when 6 million Jews were killed by German Nazis and their collaborators. They find it abhorrent that the Jewish state would expel people to face persecution elsewhere.