Big data sources do not mean the end of survey research. In fact, it is the opposite. Big data sources and surveys are complements not substitutes so as the amount of big data increases, I expect that the value of surveys will increases as well.
Researchers are now in the process of creating the third era of survey research that will most likely be characterized by 1) non-probability sampling, 2) computer-administrated interviews, and 3) linking survey data to other data. Each of these three areas are still in active development, but as the data environment changes and researchers invest more time to addresses these problems, I expect major improvements. Just as researchers took advantage of the widespread diffusion of landline phones in the 1960s and 1970s in order to modernize survey research, I expect that researchers will modernize survey research again in response to the changes created by the digital age.