As the notice says, you can pay or leave. You've tried to ask for some consideration due to your health and financial hardship, and you've got your answer, the landlord wants you to pay or leave. For breaching your rental agreement, you'll be responsible for any unpaid rent, late fees, legal fees, etc.
Many people on Avvo have asked question about the eviction process, and since lawyers devote their entire careers to it, don't expect more than a summary here of what often happens here. Basically if you don't pay or leave in 3 days, you get sued for unlawful detainer, you have 5 days to answer, a trial date is set, there's a trial, then a court order for a lock out. There are lots of variations on these procedures depending on whether mistakes are made in the complaint or in the notice or in the service of the notice or the complaint or summons, if you have defenses, how crowded the court's dockets is, etc., etc. etc.
Also, since you're in LA, you have rent control defenses under the LARSO, so research those too. Or better yet, do yourself a favor and hire a lawyer who specializes in these issues if you want to fight this notice to pay or quit.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The above answer is absolutely correct. It is also important to note that If you do get sued for unlawful detainer and you do not file an answer to that complaint within 5 days mentioned above they may request an entry of default (RFEOD) which would automatically find in favor of the Land Lord.
Do you have the rent to pay now? If so, and you want to stay, you may have myriad defenses to an eviction lawsuit, especially if your unit is rent-controlled. For instance, did your landlord ever charge you a late fee? This could be illegal, and would then be an off-set to what the notice says you owe. If the notice does not state the EXACT amount you owe the landlord, then the landlord will lose the unlawful detainer action. Did your landlord serve you with a certificate of registration? That, also, could be a defense. Did you make any repairs and not deduct them from your rent? Possible defense. Did your landlord make a mistake when he or she calculated any of the rent increases? Possible defense. Did you negotiate for your apartment in Spanish, and the Notice to Pay or Quit is in English? Possible defense.
The problem is, all you can "win" in defending an unlawful detainer action is the right to stay and pay your rent. If you don't have your rent now, and can't get it in a month, you should probably move out. There's no point in hiring an attorney if, one month later, you win the right to pay for something you can't afford.
Good luck with your job search.