The 27-year-old Honduran woman is desperate to know if the rumor is true: that she'll be allowed to stay in the United States because she is traveling with her 2-year-old daughter.

At a shelter for illegal migrants across the border from McAllen, Texas, Jennys Aguilar Cardenas and other women have heard about mothers being released with their babies, about children being reunited with relatives in the U.S. Like a game of telephone, the word has spread, giving hope to an apparently growing number of migrants willing to risk the dangerous crossing — with their young children — to escape intense poverty and crime at home.

The truth is there is no change in the law for children or parents. In practice, though, so many Central American migrants are illegally entering the U.S. with young children that there is nowhere to hold them while they wait for deportation hearings. With full capacity at the nation's lone family detention center, an 85-bed center in Pennsylvania, migrants simply are being freed with orders to appear before immigration authorities at a later time.

How many are complying with the order is unknown. A U.S. Immigration and Customs Enforcement spokesman said the agency did not have numbers available.

But as stories about releases spread in Honduras, Guatemala and elsewhere, shelter workers and Border Patrol agents are seeing more parents attempting to enter the U.S. with their children. The Department of Homeland Security has not said how many so-called "family units" it has processed this year. Officials, however, do report a dramatic spike in the number of children caught traveling without any adult relative or guardian.

Border Patrol agents in the area of southernmost Texas, across the Rio Grande from Reynosa, made more than 160,000 apprehensions between October 2013 and May, about a 70 percent increase over the same period a year earlier. Nearly one third of those detained — 47,000 — were children traveling alone. President Barack Obama last week called the phenomenon "an urgent humanitarian situation," and asked Congress to approve additional spending to house the children at two military bases.

Read more from the Associated Press at ABC News