CHICAGO (CBS) — Thousands of pilgrims have been flocking to a Catholic church in Des Plaines since Sunday night, for the Feast of Our Lady of Guadalupe.

Cardinal Blase Cupich celebrated the 5 a.m. mass Monday at the Shrine of Our Lady of Guadalupe, on the campus of Maryville Academy. He said Catholic bishops are calling for a day of prayer and solidarity especially for refugees and immigrants.

Cupich celebrated the mass entirely in Spanish, but later spoke to reporters about what he told the pilgrims.

“The bishops of the United States are also calling on public officials to make sure that we fix a broken immigration system. There are people who today are living in the shadows. We have time and again called for action, and now is the time to do so,” he said.

Asked how hopeful he is of that happening with President-elect Donald Trump taking office next month, Cupich said “We’re always a people of hope.

“We always make sure that we allow ourselves to look at what God is doing in the world, and I think that this is a just and right cause, and the truth always wins out in the end,” he added.

The pilgrimage to the Shrine of Our Lady of Guadalupe in Des Plaines is part of the annual feast day honoring the day the Virgin Mary appeared to a peasant in Mexico centuries ago. More than 120,000 Catholics, most of them Hispanic, make the annual visit to the shrine.

Many people walk very long distances for the annual pilgrimage. It started Sunday night, and will continue through 7 p.m. Monday.

The faithful said it doesn’t matter how cold it gets outside; this is the least they can do.

Some stand at the shrine for a few minutes; others for hours. They say prayers, giving thanks to the Virgin Mary, adorning her with flowers and candles.

“It’s a special day for us, because we love our Lady of Guadalupe, and every year we come here for blessings,” Nora Gomzez said as she held her 6-year-old daughter Alice.

Some pilgrims walked as long as 3 hours to get to the shrine Sunday night, despite temperatures below freezing and steadily falling snow.

“I think that they’re going to come no matter what. They’re like the mail; neither rain, nor sleet, nor snow, nor storm. They’re going to show up,” Cupich said.

From start to finish, there are 11 masses for the Feast of Our Lady of Guadalupe, but they are held inside, giving parishioners time to warm up.

One organizer said at midnight, there were at least 15,000 people gathered at the shrine. For those who wish to attend, there are four more masses on Monday; at noon, 3 p.m., 5 p.m., and 7 p.m.