Margin of error only measures precision. It doesn't measure accuracy. You can be precise and inaccurate at the same time (eg. you do this survey 5 times. estimated means are 30%,28%,32%,29%,31%, so the avg estimated mean is 30%. The survey is very precise as there is very little variation between the 5 estimated means. However, the true mean is 50%, meaning the survey is not accurate at all)
The formula for calculating the margin of error in this case is simple: ([p(1-p)/n]^1/2 ) * Z, 1-alpha, where alpha is the confidence level and Z is the number of standard deviations away from the sample mean in a standard normal distribution with mean 0 and variance 1. Plugging in the p and n, you will find that the confidence level is 95% (Z=1.96), meaning that if you compile say 100 surveys, 95 of them will report a statistic within the range of [44-3.6, 44+3.6]
Contrary to what most of you believe, 700 is a big enough sample size. The total population being estimated is also irrelevant. The credibility of this suvey depends on whether the sample taken is random and whether the questionairres are biased. NOrmally researchers also have to account for people who refuse to answer, but this survey simply bases its statistics on those who did.
So in conclusion if you want to argue against this survey, do not say that the sample size is too small. Just thought some of you should know...