I was on unemployment for a few months when I got a job offer. As it is a government job, I know the pay range. I was prepared to place near the top as I could take the hit in salary, but the salary they offered me was at the bottom of the range, half of what I'd been making before. I cannot survive on the low salary--it will not pay my bills.
The reason why I accepted was that I panicked: refusing any job offer is grounds for losing unemployment benefits and I didn't feel I could negotiate more. This was obviously a mistake and won't do this again.
I don't want to sound like sour grapes: I know how much my skills are worth and have a really tight reign on my budget, so I know what I can and cannot live on. If I stay in this job, I will not have enough money to pay my bills in about 5-6 months.
Update, to clarify: Every month I have to dip into my savings to make ends meet. If I stay here longer than 5-6 months, I will exhaust my savings. My bills are as low as they can go, so short of becoming homeless (and carless), I'm stuck.
I will need to look for a new job at a livable salary, but I don't want to screw the employer by leaving. My first week on the job, they literally said I was the best person they've ever had in this position and I did more my first week than the previous crew (of 4) did in a year.
For my expenditures, the biggest pieces of the pie are rent + insurance. Where I live, we have lease agreements, which incur an unaffordable penalty for breaking. I am taking steps to mitigate this, but I won't be able to do anything about this until next year. For reasons I won't go into, my current insurance levels are required. As for food... you'd be surprised how far you can stretch beans and rice.
My conundrum is that it isn't their fault I messed up the salary negotiation, so I want to make it right. How can I do it honorably?
Epilogue
@Wesley's answer was dead on: I discovered there was no way to negotiate any higher -- it was simply not possible to get a salary adjustment (even for market), as the salary for that position was set in stone.
Any move to another position could take months as the hiring process was very slow, and none of the available positions would pay anything close to what I needed.
I ended up lining up another job, giving my notice, and documenting everything as best I could for the next person.