If you were successful, somebody along the line gave you some help. There was a great teacher somewhere in your life. Somebody helped to create this unbelievable American system that we have that allowed you to thrive. Somebody invested in roads and bridges. If you’ve got a business — you didn’t build that. Somebody else made that happen. The Internet didn’t get invented on its own. Government research created the Internet so that all the companies could make money off the Internet.
Everyone else is also free to assume the ambiguity of the pronoun, which upon reading the full context of the speech as so many of you have kindly instructed me to do, clearly refers to the infrastructure that is relevant to you if you are business owner.
Obama's use of the word "that" was neither ambiguous in contextual meaning nor in grammatical usage.
First in grammatical usage: "That" is a demonstrative pronoun or pronominal adjective. As such, the demonstrative pronoun is closest to the noun it is describing. Obama correctly used the pronoun "that" to avoid repeating the noun "Business".
Second, as to the contextual meaning, we may look at what Obama said about government research creating the Internet. Did he mean government research needed roads and bridges to create the Internet?