The team size doesn't seem to be the main problem here. If you are currently recruiting with deadlines approaching within 1-2 months then this was a management issue. This should have been brought up earlier so you have the time to employ more staff, as it will still take any new tester a few months to get use to a new system to be of any use, but I digress.
Since you are already in this position what I would do is try and shift the mindset. Although its easy to throw testing at testers, it should be the responsibility of everyone to ensure quality software.
- If you have a deadline in 1 month, does this mean all the necessary features have been implemented and the code is now, or close to, being froze? At this point - as others have suggested - the developers can now help with testing.
- If you are still adding new features and are using agile, this is where you start dropping less important work to ensure a decent minimum viable product can be released that still satisfies the customers requirements.
Adding a new tester now will likely not help with the short term goals as you will have to spend time to hire, teach them the new system, etc.
So, my advice would be to try and make sure everyone is focused on quality. Try and get developers, managers, anyone within the company who can use the software to use it, focusing on as much coverage as possible. Good luck.
As a side note: If you have time, I suggest How Google Tests Software as it has some interesting insights into their strategy for testing very quickly and, more importantly, ensuring a quality product is delivered without having thousands of testers.