I wonder what the percentage is of those not willing to disclose the info
Excellent point. I haven't seen the questionnaire that Gallup uses (nor has anyone else outside the firm, since it's proprietary), so I can't address how they deal with the very real challenge of asking people deeply personal questions in a way that gets consistently honest responses. As far as the sample and fieldwork methodology, their summary of it is below.
On the one hand, it shows they definitely do a proper at getting to a representative sample. On the other hand, again without seeing the survey instrument (or detailed tabs of results, which again are proprietary and not available) it is impossible to make an assessment of how effectively they deal with the risk of refusal or erroneous response. That doesn't mean they don't or don't try to address that; it just means we don't how effectively. IMHO, given the sensitivity of the subject matter and the focus Gallup has on maintaining it's Tiffany-like reputation, I highly,
highly doubt they would be publishing these results if they weren't
very confident about their accuracy.
Survey Methods
Results are based on telephone interviews conducted as part of the Gallup Daily tracking survey June 1-Sept. 30, 2012, with a random sample of 121,290 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia, selected using random-digit-dial sampling.
For results based on the total sample of [national adults/registered voters], one can say with 95% confidence that the maximum margin of sampling error is <±1 percentage point.
Interviews are conducted with respondents on landline telephones and cellular phones, with interviews conducted in Spanish for respondents who are primarily Spanish-speaking. Each sample includes a minimum quota of 400 cell phone respondents and 600 landline respondents per 1,000 national adults, with additional minimum quotas among landline respondents by region. Landline telephone numbers are chosen at random among listed telephone numbers. Cell phone numbers are selected using random-digit-dial methods. Landline respondents are chosen at random within each household on the basis of which member had the most recent birthday.
Samples are weighted by gender, age, race, Hispanic ethnicity, education, region, adults in the household, and phone status (cell phone only/landline only/both, cell phone mostly, and having an unlisted landline number). Demographic weighting targets are based on the March 2011 Current Population Survey figures for the aged 18 and older non-institutionalized population living in U.S. telephone households. All reported margins of sampling error include the computed design effects for weighting and sample design.