Historically, blacks have been suspectable to bloc voting.
I have been doing some research lately on the 1952, 1956, and 1960 elections, focusing on the two nearly all-African American congressional districts that existed at that time: IL-01 (the heart of the "black belt" on Chicago's South Side) and NY-16 (Harlem, excluding East Harlem which was largely Puerto Rican--with some Italians remaining--and was in another district). IL-01 was listed as 91.7% Negro in the 1960 US Census, 91.0 in the 1960 one. NY-16 was listed as 86.8% Negro in 1950, 88.0% in 1960. Both districts were represented throughout the decade by African American Congressmen (William Dawson for IL-01, Adam Clayton Powell, Jr. for NY-16). Here are maps of the districts:
Here are the figures for how these districts voted in the presidential elections of 1952, 1956, and 1960. (I am omitting minor party candidates, who got very few votes in these districts.)
IL-01
1952
D (Stevenson) 99,224 74.6%
R (Eisenhower) 33,805 25.4%
1956
D (Stevenson) 68,266 63.7%
R (Eisenhower) 38,827 36.3%
1960
D (Kennedy) 81,399 77.4
R (Nixon) 23,109 22.0
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NY-16
1952
D (Stevenson) 82,882 81.2%
R (Eisenhower) 17,497 17.0%
1956
D (Stevenson) 62,004 66.4%
R (Eisenhower) 31,325 33.6%
1960
D (Kennedy) 58,192 64.9
Liberal (Kennedy) 11,364 12.1 JFK total: 77.1
R (Nixon) 19,902 22.2
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Now it is possible that the vote from big northern African American communities like those of Chicago an New York understate the Republican vote among African Americans in the nation as a whole--for example, the relatively few African Americans who voted in the South seem to have retained their Republican loyalty longer than those in the North. Nevertheless, even looking at the northern big city African American vote, one can say that it was not quite a bloc in the sense of the 90% plus percentages for Democratic presidential candidates we are used to since 1964--or the Republican percentages before the New Deal. Except for Eisenhower in 1952 in NY-16, the Republican presidential presidential candidate in these years always got at least 22 percent of the vote. 1956 was easily the GOP's best year among African American voters. Stevenson took a "moderate" stand on civil rights to get southern white votes; Adam Clayton Powell, Jr. openly endorsed Eisenhower, supposedly on civil rights (cynics suggested it might also have something to do with the administration dropping an income tax charge against Powell). Anyway, Ike got 33.6% of the vote in the Harlem district and 36.3% in the Chicago South Side one.
So if the Republicans in 1964 had not nominated a candidate who voted against the civil rights bill, would the African American vote be competitive? Let's say it would at least be more competitive than it is now! Whether you get 10% or 32% of the African American vote in a state matters in a close election. The problem of course is that some of the very positions that Republicans have taken that alienate black voters may have been necessary for them to win white voters in the South and elsewhere..
(One final note: If Nixon had done as well among African American voters in 1960 as Ike had done in 1956 it is quite clear that he would have carried Illinois--and very likely New Jersey and Missouri, and these states combined would have been enough to give him a majority in the Electoral College. I don't know if calling Dr. King's wife would have been enough to do that, however. One must remember that in 1960 the US was in a recession--a mild one to be sure, but even mild recessions hit the African American community hard. But in any event I doubt that calling Mrs. King would have cost Nixon a single southern state he carried. )
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Sources: Congressional Data District Book: Districts of the 87th Congress gives the 1952 and 1956 presidential vote by district. as well as the 1960 census figures by race per district.
https://books.google.com/books?id=WfZBkikMdI8C&pg=PR7
For the 1960 presodential vote by congressional district, I have used the 1961 CQ Almamac:
https://webcache.googleusercontent.com/search?q=cache:uGws4K8ypzoJ:https://library.cqpress.com/cqalmanac/document.php?id=cqal61-879-29204-1371757+&cd=1&hl=en&ct=clnk&gl=us
For the 1950 census figures on percentage of African Americans in each congressional district, see
https://webcache.googleusercontent.com/search?q=cache:uRUj0htSg1MJ:https://library.cqpress.com/cqalmanac/document.php?id=cqal56-1347950+&cd=2&hl=en&ct=clnk&gl=us