The American Family Health Study (AFHS) collected family health and fertility data from a national probability sample of persons aged 18-49 between September 2021 and May 2022, using web and mail exclusively. In July 2022, we surveyed AFHS respondents and gauged their willingness to become part of a national web panel that would create novel longitudinal data on these topics. We focus on predictors of willingness to participate, identifying the potential selection bias that this type of approach may introduce. We found that efforts of this type to create a national web panel may introduce potential selection bias in estimates based on the panel respondents, with individuals having higher socioeconomic status being more cooperative. Thus, alternative recruitment strategies and re-weighting of the subsample may be needed to further reduce selection bias. We present methodological implications of our results, limitations of our approach, and suggestions for further research on this topic.