Undocumented aliens do pay taxes

A lot of them pay federal income taxes.  A lot of them pay into Social Security as well.  It has been estimated that they pay about $12 billion a year into Social Security -- when they will not be eligible to receive such benefits, ever.  The Social Security system ends up benefiting from their contribution. 

They also pay property taxes -- either directly, or indirectly (by renting).  They pay sales tax too.