Whether formally networked together or not, a fair number of Anglican blogs constitute an effective collective promoting 'No Covenant' (some are linked to on my sidebar, including Preludium, Kiwianglo's Blog and Thinking Anglicans on a regular basis, but recently my friend and colleague Bosco Peters at Liturgy also chimed in). I suggest a casual Anglican reading around the blogosphere would likely form an impression that the No Covenant campaign was well supported around the Communion and even arrive at the conclusion that the campaign is destined to succeed.
Quite why there are few Anglican blogs such as this one which promote the Covenant I am not sure. Perhaps Covenant supporters are busy on other matters! But at risk of incurring an 'of course you would say that Peter' response I suggest that No Covenant campaign's probability of success should not be measured by its posting prolificity. In the end the arguments in favour of the Covenant are simple to explain, reasonable, and thus likely to win favour in Synods (where decisions are actually made, much as some of us might like to see decisions made via comment threads to which we contribute our self-evident wisdom).
The simple argument in favour of the Covenant is that the Communion needs to reestablish its constitutional basis as a coherent organisation. It has been exposed in the last decade as having insufficient means to engage in a guided process towards resolution of serious disagreement if not division. To the argument that no new constitutional basis for the Communion is required because we Anglicans do things less formally there is a simple reply in the context of any General Synod or Convention: if we really believe that then why not abolish the constitution of our own church, and if we think a consitution is a good idea for our own church, why would it not be a good idea for the Communion?
It is, contra quite a lot of prognostication via the internet, entirely reasonable to expect member churches governed by their own internal constitutions to accept that the growth and development of the Communion now requires a fit for purpose constitution for the Communion. What is good for the member goose is good for the global gander.
I get the point made in a comment a few posts back by Bosco Peters that 'Covenant' is not the appropriate name for what is going on. Although it is a bit of a mouthful we are talking about a 'Communion constitution.'
A final thought: why are advocates for the blessing of same sex relationships so against the Covenant? Are they projecting the weakness of their arguments onto the Covenant? If the arguments for the blessing of same sex relationships are theologically strong and biblically mandated this will be recognised by the wider body of Anglicans covenanted together to find common cause and common ground for Anglican doctrine.
In the end I think the Covenant is likely to be agreed to by most if not all members of the Communion (i.e. those still engaged in the regular life of the Communion) because it asks people to be in favour of something which is a holy and good purpose: that the Communion be a coherent global body of Christ.