"I'll run go get a taxi" (about.com)
This construction is called as serial verb one by about.com and Prof. John Lawler. While it is as catenative verbs construction by wictionry.org and CGEL: “ catenative verbs are verbs which can be followed directly by another verb — variously in the to-infinitive, bare infinitive or present participle/gerund forms. (wictionary.org)”; “which take non-finite complements (CGEL,p.104)”.
There being two ways of seeing the construction, it’s not clear whether it can be understood as ‘I’ll run and go and get a taxi’ or ‘I’ll run (to) go (to) get a taxi’. I guess there isn’t that big difference between the two. For to-infinitvals can denote sequential or simultaneous occurrence of the actions or the result of previous action - or the effect of switching scenes: I run, click, going, click, getting a taxi.
What I wanted to know is which one –– omission of and (conjunction), or omission of to (subordinator) or bare infinitival –– you natives have in your mind when you say them.