世の中は いっぱい いっぱい せいいっぱい
seems to be trying to make a rhyme here. So, it may mean more of a figurative manner and 'Life is one hurdle after another' sounds a good translation as an aphorism in my first impression when you encounter a lot of difficulties with a full energy.
- いっぱい literally means 'full'.
- いっぱいいっぱい is a set phrase and normally used to beyond one's control when one has too many things to deal with.
- せいいっぱい literally means "Full energy".
- へこたれる means gives up, so へこたれんなよ means "don't give up" or something like that.
There is a space in lyrics, so it does not explicitly say "いっぱいいっぱい” in a complainant sense and it implies a flavor of the set phrase.
Therefore, it probably implies something like "there are so many things to work on with your full energy to your limit" and "Never give up".