Tariffs on particular products tend to protect the small percentage of

Tariffs on particular products protect a few and hurt many (let's say 10 - 90)
Most oppose such tariffs.

Conclusion:
Politicians would be more likely to be reelected if they voted against these tariffs

We are now looking for a missing necessary premise:

(A) Supporters of tariffs on particular products are not significantly more likely than opponents to base their vote for a politician on the politician's stand on this issue.

Let's see what happens when we negate this - supporters are significantly more likely to base their vote on this issue.
Then supporters of tariffs will vote against the politician who stands against tariffs.
But opposers of tariff may not give any preference to the political who stands against tariffs.
So my standing against tariffs, the politician may get no extra votes (since tariff opposers give her no preference) but may lose some votes (because tariff supporters don't like her). Then the politician will not be more likely to be re-elected. This is an assumption.

(B) Politicians always vote according to what is most likely to get them reelected.
The argument does not say that the politicians vote against tariffs. If it did, then we would be assuming that they vote according to what is most likely to get re-elected. It says that "politicians would be more likely to be reelected if they voted against these tariffs." We are not assuming anything about what the politicians actually do.

(C) Politicians should support only general tariffs, since such tariffs would be more widely popular with voters than tariffs on particular products.
General tariffs and what the politicians should or should not support (ethical question) are not topics of discussion. The topic of discussion is what would make politicians more likely to be reelected.

(D) Politicians should never support measures that favor only a small percentage of the population.
Again, what the politicians should or should not support (ethical question) is not the topic of discussion. The topic of discussion is what would make politicians more likely to be reelected.

(E) People who would be hurt by tariffs generally know that they would be hurt by them.
We are given "Polls show that in fact most people oppose such tariffs". This is what the argument is based on.

Answer (A)