If you get no government assistance, you meet your own needs independently....
What about tax breaks? If I'm getting a tax break on the interest payments for my mortgage, is that not a form of "government assistance?"
How about farm subsidies? I'm pretty sure if we disenfranchised every farmer who takes a subsidy, it'll be a lot easier to reduce the costs of the farm bill.
How about public transportation? Millions of Americans rely on public transportation systems that usually run at a loss. Do you lose the right to vote if you don't own a car?
Oh, wait. If you own a car, then you're using highways built, owned and operated by the government. Why isn't that classified as a handout?
Children get no vote because they're fully dependents of others.
The reason why children don't vote is because they have not reached the age of majority, and are not considered mature enough to accept the full range of rights and responsibilities.
Adults on public assistance are usually somewhere in the gray area, so their votes should be weighted.
So a veteran who can't find a job, and goes on food stamps, is a dependent sort of like little child? Someone who gets in a car accident and is paralyzed from the waist down ought to lose their vote, because they can't work and must depend on others?
What about a 58 year old factory worker, whose company closes the factory he works in and moves to Mexico? Should he lose the right to vote because he chooses to collect unemployment in order to make ends meet? Even if he is willing to work, and jobs are not available?
There is no "gray area." Receiving TANF, SNAP or unemployment insurance does not mean you are a lazy slob who refuses to work and will vote for Democrats forevermore. For many people, it's the only way they can keep their families fed.
The sad thing about all this is:
If conservatives / Republicans could actually draw voters with their policies, they wouldn't be looking for excuses to disenfranchise citizens.
The premise here is that people will vote in their own self-interest. Why don't conservatives and Republicans offer policies, then, that help the poor -- instead of finding reasons to bar them from voting? It sure sounds like you're just writing off the poor altogether, instead of thinking of them as actual human beings and actual citizens, with genuine political interests.