Sample size vs response rate, which is more important? While I was preparing an internet survey, I read from multiple sources which says it is more important to have a high response rate than large sample size.
Q1. I don't quite understand the logic behind this. Can you explain? If i can afford to survey the entire population, would that be better than a random sub-sample?
Also, the importance of random sampling is often stressed. 
Q2. But what if I just invite the entire population of interest to the survey (because I can... using the internet). Wouldn't this be better than random sampling (even though the response rate might be lower because N is larger?)
I understand the answer to the questions above might depends on the objective of the study. If this is the case please delineate this for me. Thank you!
Update
After seeing seeing several responses, I guess I have asked a misleading question. I am not comparing response rate and sample size as in a contest of which is more important. I am trying to find out, if it costs me nothing more, relative to random sub-sampling, to survey the entire population of interest, is there any reason why I shouldn't do that and stick with a random sub-sample instead?
 A: The problem is that bias is not overcome by a large sample size.  A survey of 100 randomly chosen subjects with a 1.0 response proportion would yield much more valuable information that a 0.10 response fraction from 10,000 subjects surveyed, yielding 1000 subjects responding.  Suppose for example that one were estimating the probability that opinion X is held and the true probability is 0.05.  A 0.95 response fraction would yield an estimate of 0.0 if only persons not holding opinion X responded.  The estimate would be off by huge relative amount.
A: You are assuming that non-respondent data are missing at random (MAR).  MAR is a very strong assumption, and not generally borne out in practice.  You already know that respondents and non-respondents differ on at least one crucial dimension: non-respondents sent your instrument/link/request (whatever you might have used) to the bit-bucket.  Respondents did not ignore your request.  
If (and only if) you can show that data are MAR, then drawing a large sample and accepting the returns as a random sample makes sense.  The problem is that you cannot show this without investigating the non-respondents, that is, by doing follow-up work.
In fact, the situation is worse than Frank suggests above: large and non-random samples are more likely to have large biases than smaller, random samples.  Self-selected samples are rarely, if ever random.
I'll give you exactly the same advice I give researchers at my university when they propose ridiculously large samples without follow-up: don't do it.  Take a realistic sample that is random on the appropriate levels.  Plan to do follow-up, and be ready to be as big a pest as you must be to get the data.  Don't be above bribery (that is, offering incentives to respondents) to get the data.  Shoot for a response rate in the 90% range (it can be done, if you have the resources).  
It's getting a little long in the tooth, but Lessler and Kalsbeek, Nonsampling error in surveys is still a good go-to reference on these issues.
Responding to your update:
Yes, it matters.  It matters for follow-up purposes.  Suppose that you can draw a random sample of $n=100$ or a census of $N=10,000$, with a deterministic response rate of 80% in either case.  In the case of random sampling, the non-respondent group has 20 members.  In the case of the census the non-respondent group has 2,000 members.  If you have no intention of doing any follow-up no statistician I know can help you.
If you do intend to do follow-up (and you should), then in the case of the sample a census of the non-respondents is feasible.  You can be as big a pest as necessary to get those 20 observations.  Follow-up of 2,000 is a different issue entirely.  Do you propose to draw a sample of those to reduce the number to something manageable?  If so, why didn't you just sample in the first place?
