I manage somehow: slightly negative connotation, that the person is struggling with something and is just getting this to work
I can handle it: neutral / positive connotation, the person can do it
I get by: neutral / negative connotation, the person is doing it / making "it" work
I'll get by: neutral connotation, future tense the person will make it work. to me doesn't have negative feel of "I get by"