The Baikal-Yeniseian region, after the departure of groups that headed to North America, became the incubator of four language families – Turkic, Uralic, Yeniseian, and Tungusic – which had strong influence over three other Asian language families: Amuric (Nivkh), Itelmen, and Chukotko-Kamchatkan.
Some big advances have already been made in linking the Asian families just mentioned to the related North American language families. Edward Vajda has successfully shown that Yeniseian and Na-Dene are sufficiently related to merit calling them a single family, “Dene-Yeniseian.” Sergei Nikolaev has reconstructed a proposed proto-language for Nivkh, Wakashan, and Algonquian. I think I have shown that Tsimshian language is a direct descendant of Itelmen.
But a general problem in these attempts is that they have been too isolating. At the times of separation, which range from 14,000 to as little as 1,500 years ago (the latter for the separation of Yupik from Chukchi), the Asian languages on the list had usually not yet separated from each other. Between 14,000 and at least 9,000 years ago, the language most likely spoken in the Baikal-Yenisei region was something we could label Proto-Turkic-Uralic-Yeniseian-Tungusic-Almosan-Dene, and even that is an abbreviation. (I propose that this be called Baikalic.) For this reason, I suggest that the main reason for difficulty finding lexical correspondence is that so much differentiation and mixing has occurred within Asia and within the Americas over the long time period.
The linguist Joseph Greenberg proposed two large and related macro-families that he called Eurasiatic and Amerind. Both have been roundly rejected by historic linguists and I am absolutely not resurrecting his proposal. I am proposing a far more limited macro-family that emerged from the Baikal-Yenisei region and extended only to those North American groups that have proven genetic descent from the Baikal-Yeniseian region. I do think that real commonalities of languages within this group, such as agglutinative suffixing morphology with counting classes and an animate-inanimate gender system, provided Greenberg with the backbone of his overly-grand proposal.