What effects would this have on the map?
This would not have happened. The quote below is from Robert Kaufman's
Henry M. Jackson: A Life in Politics:
Jackson regarded McGovern's impending triumph [at the Democratic Convention in Miami Beach, in July 1972] as an unmitigated disaster for the party. . . . [H]e stoutly resisted the inevitability of the McGovern candidacy by all means at his disposal right up until the Democrats nominated McGovern in July. Supporters of Jackson and Humphrey, southerners, and organized labor had banded together in an abortive effort called "Anybody But McGovern." . . . Even when Muskie and Humphrey formally bowed out, Henry Jackson would not. He received 536 votes for the nomination on the convention floor. I. W. Abel, head of the United Steelworkers of America, nominated him. Governor Jimmy Carter of Georgia seconded the nomination.
Scoop Jackson's positions on the Vietnam War were amongst the most hawkish, even for Republicans. Jackson was a bigger Cold Warrior than Nixon and was critical of Detante. McGovern's whole candidacy was about the War. It would have been easier, and more coherent, for McGovern to have selected a running mate such as J. William Fulbright (D-AR), who signed the Southern Manifesto and did not support all Civil Rights legislation but who personified Democratic opposition to the Vietnam War in Congress. (McGovern never considered Fulbright but he DID consider powerful Rep. Wilbur Mills (D-AR).
You can't win a primary on a key issue and then pick a running mate who is diametrically opposed to your stance on that most important issue. McGovern-Jackson would have been a ticket that fell apart in mid-campaign. The differences on the war may have been so great that Jackson would have resigned from the ticket in mid-campaign. Jackson gave a perfunctory endorsement to McGovern and made an appearance with him, but he did not vigorously campaign for him, and it may not have worked out well if he had.