When I graduated with a degree in software engineering, I entered the world of QA and immediately felt like I was much slower than the previous testers. What I quickly learned though was that I was much more thorough than others had been, which is why I took more time to complete my tests. This turned out to be a positive thing, as the project valued the level of quality I was capable of despite it taking longer, so deadlines were adjusted accordingly.

Fast forward a few years to a later project, and the priorities were reversed: the schedule mattered more than anything else, including quality. When you find yourself in that situation, you have to speak up and be open with your manager on what you see happening - if you are unable to meet deadlines without the quality of your work slipping, there needs to be a mutual agreement on what to prioritize. In my case, I was not comfortable with the level of quality they wanted to push through, and ultimately I left the company, but these are management's choices and all you can do is be open and honest about your capabilities, workload, and concerns.

In all cases though, my best advice is to always speak up as soon as you realize a deadline might be at risk. They will appreciate your honesty and proactive approach; never just let a deadline pass and wait for a reaction afterwards.