That's right. A state legislator in Texas has introduced a bill to instruct law enforcement to turn over custody of undocumented immigrants ("illegal aliens") to members of Congress. (ht ThinkProgress » TX Rep Introduces Bill To Allow Police To Leave Undocumented Immigrants At Lawmakers’ Doorsteps).
Rep. Lois Kolkhorst (R) told reporters “I want us to take these illegal immigrants in custody to a congressman’s office and say, ‘ We don’t know what to do with these people. Do you?”
Full text of the rather short bill here [PDF], but the relevant portion is:
A law enforcement agency that has custody of an illegal immigrant to whom this article applies may:
(1) release or discharge the illegal immigrant at the office of a United States senator or United States representative during that office ’s normal business hours; and
(2) request an agent or employee of the United States senator or United States representative to sign a document acknowledging the release or discharge of the illegal immigrant at the senator ’s or representative ’s office.