Such a program is a major part of President Obama's Precision Medicine Initiative. The NIH is funding 5 research pipelines throughout the country (4 at universities, 1 at the NIH) with the intent of collecting the full genomes and accurate phenotypes of one million individuals, with ability to recontact for further information if needed. The NIH just announced the grant winners two weeks ago so the grant recipients are just starting to work on the full protocols/pipelines now.

As someone who works in the field, the lack of phenotypic data available accompanying genome sequences is currently one of two major roadblocks in advancing genomic science (money is the other problem, of course).