Your mom has rights as a tenant, and evictions must follow the law.
Eviction notices in most states require a certain amount of notice -- like 30 or 60 days. So even if you get a notice on Monday of next week, you likely have four weeks or possibly more before they would actually attempt to have you evicted. THEN, they usually simply initially TELL you to get out. You can haggle with them and say it'll take a couple of days to move etc, so that adds more time as well.
But definitely first talk to the landlord, tell them the money is coming but that there's a delay, and that now that your mom has a job there shouldn't be any more delays in the future. Most landlords prefer to keep existing tenants than to replace them, and will work with you. A simple late rent payment doesn't usually result in an immediate issuance of an eviction notice. They will typically tell you your rent's late, then set a deadline, and after the deadline THEN they will issue an eviction notice.
Even if it gets as far as an actual eviction notice and the full 30 days (or whatever) has passed, you STILL have rights that are stronger or lesser in different states. Legally evicting someone can often take a long time, although most people don't know about it and will simply move out under the assumption they have no recourse. You can claim certain rights based on having lived there a certain amount of time, having paid a portion of the rent already (a key point, so if your mom can pay ANY of the rent at first, even a small amount, she should do so since it makes it MUCH harder to evict in that situation).
If all else fails, check the lease -- it'll state when evictions can happen, but it also states the responsibilities of the landlord. If the landlord is in violation of any of their responsibilities, like fixing things or ignoring requests that you have a right to make as a tenant, that lone is actionable in terms of delaying an eviction (since non-payment of rent can be legal when it's due to a contract violation by the landlord). That's one delaying tactic, if it becomes necessary to delay. Document the landlord's violation of the lease (and most landlords in fact commit lease violations, people just tend not to act on it), and let them know that you are withholding rent due to the violation until the situation is resolved.
If you refuse to vacate after all of the above, you can still force the situation into court. Take copies of the lease, your letter to the landlord noting his/her failure to meet their responsibilities, a copy of a check or something showing you did pay at least a small amount toward the rent, a written explanation of the financial problems that led to the inability to pay the full rent, and a written explanation of how long you've lived there and how you are making efforts to meet your obligations and that you challenge the claim that they have a right to evict you etc.
All told, if you do it right, you can delay an eviction for a LONG time. Look online for the laws in your state about tenant's rights and how much advance warning you must have for an eviction. The landlord almost surely needs to get an actual court judgment to legally toss you out, in most states. The eviction papers must be written in a very specific manner, notice must be given a specific way, and there are lots of laws and rules the landlord must follow. Any failure to follow the laws and rules will help negate or delay an eviction. So if things get serious enough, you really should look into all of this in detail.
Lastly, there are attorneys and groups that provide assistance -- often free of charge -- to tenants. You should look into it and see if there are any such lawyers/groups in your state, and contact them if there are. Sometimes you can even look up a local attorney in the phone book or online who specializes in tenant's rights and housing law, and just call them to see what they might recommend. Usually an attorney will listen to your basic situation, and they will often give you some initial basic advice. It's always worth a phone call for some free suggestions from a lawyer.
I hope things work out for you and your mom. It sounds like you can talk to the landlord and at least ask for an extension and then pay at least a small amount of money toward the rent, and they almost definitely would not issue an eviction notice until at least a week or so later at the earliest. By then, your mom will be working and surely will get paid at the very latest by the end of the month -- which presumably will be within the time frame before they could actually come and try to make you leave (since after the eviction notice you should have about 30 days, depending on the state). So if she'll have pay within a couple of weeks or so, and if you can at least pay a small fraction of the rent (any amount is helpful), and if they agree to give you just a slight extension, you shouldn't actually be in any real danger of getting evicted. And obviously, if your mom will get paid weekly or bi-weekly, she'll definitely have the rent money in plenty of time even if an eviction notice is issued next week.
