Importance of the current postdoc advisor's letter in TT job search I have strong publication record in my Ph.D. and 1st Postdoc that went for two years. Got 4 TT interview calls before last year.. but not successful in any. Last year did not apply, but this year, after fixing a few shortcomings noticed in my previous interviews, started the search again. In the meantime I published a couple of top journals as the corresponding author. However, I am not in harmonious professional relation with the present postdoc advisor. I am working for a little over one year in this position but did not yield any journal publication. I am sure that this advisor's reference will have negative impact on my search, if at all he agrees to write one. The only best way for me is avoid this advisor's letter, since I can arrange the required number of good letters from my previous affiliations. If I proceed with out my present advisor's reference, will it have any bearing on my chances? Expecting some suggestions from the people having experience in search committees.
In my view, strong letters are extremely important. You certainly don't want any letters from people interested in sabotaging you in any way. Even poorly written letters can be a setback. So can letters written by non-native speakers who may not grok the nuances of certain phrases. 

There is the concept of Damning with Faint Praise that can be absolutely deadly in a letter. It can be intentional or not, actually. 

Get letters from people who know your potential and are willing to speak for it. They need to know about your past work, of course, but people will be looking for potential and how it relates to a particular position. 

If you have any doubts about what a person might say, ask them about it, or go elsewhere. In certain situations (non-native speakers, say) you might even request that a letter writer check their letter with a neutral third party, such as a department head. This would have saved me tremendous grief long ago.