What is the function 就是 and 对 in 这个重大责任， 就是对民族的责任?
"这个重大责任， [是]民族的责任。" - "This major responsibility, [is] the people's responsibility "
"这个重大责任， [就是]民族的责任。" - "This major responsibility, [exactly is]
the people's responsibility "
"这个重大责任， [就是][对] 民族的责任。" - "This major responsibility, [exactly is] the responsibility [to] the people"


In all cases, '这个重大责任' is the topic of a [topic + comment/opinion] sentence 

The comment/ opinion:


1b. '是民族的责任'" (is people's responsibility) is the comment on the topic  
2b. '是' = 'is' ; '就是' = 'exactly is' ; '就' has many meanings. However, in this sentence, it means 'exactly', which emphasize the verb '是', not only "it is", it  "exactly is"
3b. '对'(toward) = 'to' ; it is a preposition that indicates which object this responsibility is for


民族的责任 = the people's responsibility 

[对]民族[的]责任 = responsibility [toward/ to] the people

Rephrase in English grammar: "This major responsibility, is the responsibility to the people"