And the president has said he supports Sensenbrenner's bill.
A recent immigration reform bill passed by the House in December is drawing sharp criticism for its provision mandating the construction of a fence along the nearly 2,000 mile U.S.-Mexican border. President Bush has spoken in favor of the bill authored by Rep. F. James Sensenbrenner (R-Wisc.), known as the Border Protection, Antiterrorism and Illegal Immigration Control Act of 2005. Bush has already signed legislation appropriating more than $70 million to install new barriers and improve existing protective infrastructure along the border. This includes fencing as well as vehicle barriers and lighting to enhance border security.
http://www.colum.edu/students/reservoir/studentlife/february2006/week1/borderfence0206.htm
Bush hasn't vetoed a bill yet - therefore he must be supportive of EVERYTHING Congress passes.