Are these True fallacies or a subset of another fallacy?

In the course of my life I've discovered that when people want to torpedo somebody elses ideas they have a tendency to use one of these three favorite rebuttals.
In these examples I've used "Sidewalks" and "Homeless people" you could drop in any other combination you want and the result would be the same. But they always have an appeal to sympathy buried in them. I'm curious whether they're really fallacies, or just verbal fastballs to throw you off your game.

The first runs along the line of what I call the "Greater good fallacy". The 'fallacy' always runs along these lines. Why are we spending money on studying cracks in the sidewalk, when we have homeless people in America. Think of all the good that could be accomplished if we spent it on them spent on them first?

The next one is what I call the 'bait and switch' fallacy. This runs along the line of "Normally I'd be all for studying cracks in the sidewalk, in fact no one is more interested in cracks in the sidewalk than I am (I almost tripped and broke my leg the other day <An appeal for sympathy here> Of course, this is the bait) however when you think of all the homeless people in america shouldn't we spend the money on them first? (And then the switch).

And finally the 'We've got to get our priorities in order'. Why are we spending money on studying how cracks develop in sidewalks when there are homeless people in America. We've got to get our priorities in order.

As you can see they're all fairly effective at disarming the speaker and putting one on the defensive.

As I believe I have argued fairly consistently on this forum, I am a generally a believer in fewer, rather than more Logical Fallacies, i.e., that are applicable to situations or problems that have been presented by Forum questioners. Of course, everything is case specific but IMOP, you really need to have a true violation of logic (i.e., of a logical ARGEMENT) present to justify the presence of a Logical Fallacy. (Bo, citing ‘informal’ logical fallacies, may disagree.)

The three examples you bring up are quite similar; however, subtle differences in phrasing may determine whether logical fallacies are present. Sequentially,

1.“Why are we spending money on studying cracks in the sidewalk, when we have homeless people in America. Think of all the good that could be accomplished if we spent it on them spent on them first?” - This is a common argument and traditionally trades off ‘Guns vs. Butter” (Military spending vs. feeding the poor, social programs, etc.). There is no logical fallacy present here, since with a finite amount of money to be spent, the issue becomes PRIORITIZATION of spending, which is entirely subjective. This subjectivity does not change if ‘sidewalk cracks’ are substituted for ‘Guns’.)
2.“This runs along the line of "Normally I'd be all for studying cracks in the sidewalk, in fact no one is more interested in cracks in the sidewalk than I am… however when you think of all the homeless people in America shouldn't we spend the money on them first?” -This, as stated, is essentially a non sequitur argument, since it does not follow that either: a. homeless needs could be meaningfully improved with advance spending (in a comparable amount) and/or b. the utilitarian ‘good’ accomplished by sidewalk spending (preventing accidents in perpetuity) may be less than highly temporary relief for the homeless (at a modest expenditure.)
3.“We've got to get our priorities in order'. Why are we spending money on studying how cracks develop in sidewalks when there are homeless people in America. We've got to get our priorities in order.” – No Logical Fallacy. Again, these “priorities“are highly subjective, and as such this does not constitute a Logical fallacy.

"Greater good fallacy": I don't think this is fallacious as you have worded it. Asking "why should we devote resources to A when B is more deserving of our resources?" is a perfectly valid question. The answer can also get into some deep philosophical musings such as the classic, "Is it wrong for me to spend money on luxuries when so many people are starving in the world?" I could get into how human well-being is multidimensional, but this is far beyond fallacies. The bottom line, it is not a fallacy. Someone can commit a fallacy when attempting to justify why they think A deserves more resources than B (or vice-versa), but we would need to see that justification attempt.

"Bait and switch fallacy": Same as above, but it appears that some extra rhetoric is being used (i.e., what you call the "bait"). Again, I see no fallacy, just powerful communication/persuasion techniques that sets an empathetic tone.

I would charge non sequitor, what we spend on homelessness has nothing to do with whether spending on sidewalk repair is an efficient use of resources.

The respondent is introducing a different argument, he is arguing for prioritization of resources, which is highly subjective.

Here's what I see:

Argument
P1: Sidewalk cracks are a hazard to the community.
P2: Fixing sidewalk cracks requires money.
P3: It is our responsibility to fix sidewalk cracks.
C: We need to spend money fixing sidewalk cracks.

Counter-argument
P1: The homeless problem is more of a hazard to the community than sidewalk cracks.
P2: We cannot spend money on both issues.
P3: It is our responsibility to fix the homeless problem.
C: We need to spend money on the homeless problem and not on fixing sidewalk cracks.

Both arguments are sound. People will argue that one or the other isn't valid, based on their perception of the truth of any of the predicates. How these positions are argued does not change the actual arguments. I would suggest that any of the predicates can be either true or false.

A specific argument of this kind that I hear is "Why are we spending money on refugees when we have homeless vets right here?" My argument suggests that P2 of the counter-argument above is false; we have enough resources that we can devote some to each issue. I know (and fear) that many people would suggest that P3 of the main argument above is false; it is not our responsibility to help refugees.

I see no fallacy; I see lots of questions about the assumptions each person is making.

I think it is appropriate to address the problem of the initial question 'Are these True fallacies or a subset of another fallacy?'

The problem of what is a fallacious argument is not a question of what is true or false. Something false or true may be the conclusion of a fallacious argument, because the argument is unsound and a flawed argument.

After reading everybody's thoughtful comments and thinking about it some more I think all three of the examples that I presented fall into the general category of the "False Dilemma" following the truncated form of "If we spend money on X then Y will suffer as a result. Do you really want 'Y' to suffer?".