The four are now split between two households, and between those who expect to stay and those who would return to Ecuador  a tally that keeps shifting. The daughter, despite tireless efforts to get ahead, feels she is losing ground and worries that her brother takes his citizenship for granted. The son, despite his freedom, carries the weight of his family’s highest hopes.

Their status is also mixed in less obvious ways. The mother, 47, who gave up her fledgling career in Ecuador as a computer systems analyst and now baby-sits for a living, has not had anywhere near the same opportunities in this country as the father, also 47, who found rewarding work as a draftsman. Increasingly dissatisfied, she has tried in vain to leverage her son’s citizenship to get a green card granting her permanent residency.

Still, they are a loving family, and better off than many illegal immigrants, making a comfortable life in a city that welcomes foreigners, with or without papers. The parents are among a rising proportion of illegal immigrants with higher educations  at least one in every four are believed to have had some college  abandoning careers back home to try to vault their children into the American middle class in a single generation.

Yet as each year brings new setbacks, they hear the clock ticking and push their children harder. For all the daughter’s high ambitions, the mother never misses a chance to point out a simple solution to her career impasse: find an American husband.

One Saturday night last month, the family gathered to celebrate the daughter’s 22nd birthday in a Chinese restaurant where most of the tables were filled for a raucous wedding reception. As they waited under the swirling disco lights for dishes of pork and seafood, the parents asked the children about their plans  for school, for work, for life.

The son was characteristically vague, saying only that he wanted to attend college. The daughter, as usual, had her future worked out in fine detail: graduate school, community work, a life of service and independence.

But they could barely be heard above the dance music pounding through the restaurant. As a toast was raised to the bride and groom, the din grew louder. Dozens of guests clinked their spoons on glasses.