The second-ranking Republican senator's visit Monday comes as Congress grapples with comprehensive immigration reform. Cornyn has praised some aspects of the bill put forward by the Senate's bipartisan so-called Gang of Eight last month, but criticized it for not going far enough to improve border security.
Cornyn has long called for improvements at the ports of entry on the Southwest border, both in terms of security and trade.
Monday's meeting was scheduled to be held at the Rio Grande City port of entry.
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