On the surface, the Nandrajogs are a thoroughly American immigrant success story.

Harinder Nandrajog is an IT professional, and came to the US in 2011 on an H1-B visa. He brought along his wife, Ekta, and their two young daughters, who came legally on H4 visas as his dependents. They settled into life in Weymouth, and Harinder’s employer sponsored their green card application, which was approved in 2013. But they’re still waiting for those green cards, and the delay is splitting up the family.

When Meenakshi, the Nandrajog’s eldest daugher, graduated from Weymouth high school last spring, she planned to stay at home and commute to college.

“She actually got admission into U-Mass, and she got scholarships, and she got free tuition fee for all four years,” Harinder recalled.

But they soon found out that Meenakshi was disqualified from receiving those scholarships. Because they’re still waiting for those green cards, Meenakshi was technically a foreign student. That led to a scarier realization: even if they could afford to pay the tuition and foreign student fees for the University of Massachusetts, Meenakshi will turn 21 and have to leave the country before graduating.

Ekta Nandrajog said the safest bet was to send their daughter to college in Canada.

“Today I was talking to her, and she [said], ‘When I tell everybody that I'm from Boston, they all make fun of me like, 'From Boston you came here to study? Because Boston is hub of all the colleges and all and you are here?'" she recounted with an ironic, unhappy laugh.

Meenakshi only recently left for Canada, and the feelings are still pretty raw.

The Nandrajog’s younger daughter Shourya, a 10th grader at Weymouth High, said she misses her sister “a lot, but I feel like she will have a better future there, because she can work there.”

The H4 visa means the Nandrajog kids can’t legally work in the U.S. “She already has a job there so she can like pay off her fees and it's just, like, easier for her, and probably easier for me too if I go there.”

More than 600,000 Indian immigrants are waiting for green cards, according to David Bier of the Cato Institute. Bier has written about the reasons Indians, in particular, face this delay. He said that when tech workers apply for H1B visas, there are no limits on individual countries. Given India’s population and education levels, that means a lot of Indians are coming to work in America.

But Bier said Indian families applying for permanent residency face a quota: no nationality can receive more than 7 percent of the green cards issued in any given year.

“You have 1.3 billion people living in India," he said. "They received the exact same quota as Estonia, which has 1.3 million people,” — 1,000 times less.

Bier worked out the math on what the backlog means for people like Harinder Nandrajog.

“If you look at people with advanced degrees right now, going forward you're talking about a projected 151-year wait,” he said.

There’s wide bipartisan support for legislation that would address the backlog— a version even passed in the House in 2011— but the bill never made it to the Senate, and it’s been stuck in congress since then.

The wait has proven heartbreaking for the Nandrajogs. Canada isn’t that far away, but the family’s mixed legal status means there won’t be any visits home anytime soon.

“She is there, but she cannot even come to see us, because she needs a H1 visa stamp on her passport,” Harinder explained. “So that is another difficulty we are going to face in future. So now we are out applying for a visa to visit to Canada. We'll go to see her …” he said, becoming emotional over the thought of missing his oldest daughter. He had to leave the room.

Ekta said the separation has been hard on him, “the father-daughter” relationship being a “special” one.

Preserving those relationships might mean giving up on the U.S. Before either daughter turns 21, Harinder Nandrajog’s work visa will expire, and he said with all the uncertainty, he may not bother to apply for an extension.

Editor's note: WGBH News reporter Arun Rath followed up with another family facing visa problems, the Kumars. Here's a Greater Boston segment on the Kumars' story.