First of all, you should evaluate the work lead and prepare a report that justifies your request for hiring more employees. Make sure your points are valid and appropriate as it will help you in getting the attention and consideration of your boss.
If your organisation is passing through a difficult time and your boss is reluctant to hire new staff, then you have to convince him with strong and logical points and make him realise that this is the only way that can help in getting rid of this difficult situation.
You should present your boss with complete details of workload and available workforce because it will help him in understanding the seriousness of the issue and the result will be in your favour.
You should include compelling points in your report that an addition of certain number of employees can help in getting more production which will be helpful in getting the company out of crisis.
Also convince your boss that hiring a few people will also help in getting an edge over the competitors in the market. It will convince your boss and there stands a firm chance that you get your request approved.
Make a feasibility report stating that you will generate more productivity after increasing the number of your staff members. Also ensure your boss that it will also be cost effective and in no way will have any negative effect on the growth of organisation.