[movies]

You mean something like this?

[HP]

Perfect example for anionic polymerization movies! But as i see this wonderful scheme you show the Nuc attack of HO:- as i understand but then what happen with the H from the water or  where it goes? If happens this reaction H-OH + H2C=C(CN)COOR --> HO-CH2CH(CN)COOR do you mean the forming CH is very acidic and if so may be next reaction with H2O qould lead to H3O+ and the obtain the anion? Also do you think its possible and "migration"polyaddition mechanism of polymerization of cyanacrylate as just this CH proton migrate from monomer-to-monome to polymer In fact from my studies i know the mechanism of polymerization is exactly as you show by  anionic polymerization and thats why so quick and efficient but who knows;)
Thanks again!
HP

[movies]

You probably need some catalytic amount of base to initiate the reaction.  The proton between the two withdrawing groups is less acidic than hydronium (H₃O⁺).

You might get some product just base on the equillibrium between the protonated and deprotonated forms, but base would definitely be a good idea.

[HP]

Well hope still in the topic
How really to form carb anion of cyanacrylate monomer only with very small amount of water absorbed by air moisture on the surface we wont to stick. I am hinking about these hypotheses:
First addition of H2O to cyanacrylate to intermediate HO-CH2CH(CN)COOR
As you see there's 2 mobile protons of this molecule CH acidic and OH - i dont know   Do you think its possible these quick post reactions:
HO-CH2CH(CN)COOR + H2C=CH(CN)COOR--> HOCH2C:-(CN)COOR(methylol substituated carb anion 1) + H3C-C:-(CN)COOR (2nd methy substituated)
Also if HO-CH2CH(CN)COOR - H2O--> H2=C:-(CN)COOR monomolecule disproportion but then i am not specialist if this resonanse structure is possible or how stable?
And last i can imagine now for really in situ Michael addition of intermediates:
HO-CH2CH(CN)COOR + H2=C(CN)COOR--> HC(CN)(COOR)-O-CH2CH(CN)COOR which somehow to form bi-anion which should be very active and would make the polymerization twice faster  
Now i am searching for some research works onto the cyanacrylates polymerization mechanism problem and if find something will share you.
Ops i think i have mistake in water addition to cyanacrylate
H-OH + H2=C(CN)COOR--> H3C-C-OH(CN,COOR) Is this by Marcovnikov rule?

[movies]

The addition of OH will be anti-Markovnikov in this case because of the withdrawing groups.  The beta carbon is much more electrophilic than the alpha carbon (draw out the resonance structures and you will see why).

To initiate the react you could add some aqueous NaOH.  You could also use a different basic, nucleophilic activator like sodium methoxide or sodium acetylacetonate.

The proton of the alcohol in the OH + acrylate aduct will be a lot less acidic than the proton between the two withdrawing groups (pKa of about 16 and 12, respectively), so addition of the oxygen instead of the carbon would be unlikely.

[HP]

You are right for anti-Markovnikov addition. But at the literature no such water addition described( i mean to Michael product HOCH2CH(CN)COOR) but its always given aduct as on your scheme HO:-(base from water) + H2C=C(CN)COOR--> Base-CH2C:- and so on anionic polymerization of cyano acrylate monomer by classic mechanism...To virtue the fortune of H+ from water which is surrounded by very big excess of cyanoacrylate molecules than water theres may many possibilities by my view: H+ H2)--> H3O+ or may be H+ + CN --> ?
Also no to forget the last ethap of every not living polymerization : termination of the polymerization process..I suppose one of the end-groups of the "died" polymer chain should be HOCH2C(CN)COOR-- and on the other end --CH(CN)COOR  
In the literature write the polymerization cyano acrylates is initiated also by nucleophiles like akcohols and amines. Well in this view i think its hard in situ to obtain RO:- or RNH:- and only  Michael addition possible what do you think   R-O-CH2CH(CN)COOR and then polymerization mechanism may be much interestin
Continue thinking...

[HP]

Sorry for the stupids i wrote with water as base HO:-  actually the basic is unshared el pair at O-athom so H2O:(base) + H2C=C(CN)COOR--> +H2O:-CH2C:-  :
But the possible addition of H from water by Michael is also possible reaction what do you think  

[movies]

Yes, it could be water, perhaps.

As to the termination of the polymerization, it probably occurs via alkylation with some terminating species (e.g. MeI) or, as you suggest, by protonation of the carbanion.

I don't understand what you mean by saying that things like MeO- are hard to obtain.  NaOMe can be made easily with methanol and NaH.

[HP]

Hi
And now if the oxa-Michael adition is possible with strong electrophils like alkoxide then i am thinking what happen with the alkali athom in conjugation with acrylic compounds for example:
R-O:-Na+ + CH2=CH-COO:-Na+--> R-O-CH2CH:-(Na+)COO:-Na+<-->
R-O-CH2-CH=C(O:-Na+)2
What do you think about the possible resonance structure of CH-COO segment is it possible  
Thanks

[movies]

Well, once you have a carboxylate anion for the acrylic acid the Michael addition will become very difficult because the C-C double bond won't really be activated anymore.  It would be like trying to add RO-Na to 1-butene.  Really hard to do!

[HP]

Hah the theory is grey  but green the tree of life
My first experiments this reaction show very good yelds of oxa-Michael product
and i am encouraged that...
Very good discussion and pleasure for me! Hope was interesting for you and useful for all...
Regards