So how do you inspire developers to execute in a timeframe dictated by others? You have to be a leader who inspires the engineers to complete the task, even if it requires putting in extra hours. This means setting the example, looking out for your engineers' welfare, being able to provide answers and not problems, and being someone who can be easily approached.
The moment something goes wrong, the burden is on the manager to make the right decision - the wrong decision can have negative ramifications over months, if not years. The moment you micromanage, something is broken in your process, or with the people involved.
I recently had to start wearing a technical lead & director hat - the intense pressure of the startup world bore down on my whole team in order to get a working product in order from scratch in about 1 1/2 months of coding. The resources became scarce since the technical lead got sick & had a family death, while two other senior engineers had babies in the time period. It then was left to two junior developers and me to do the lion's share of work until the other engineers could get back to work. I let the junior engineers work mostly normal hours (until close to our deadline) - I ended up taking the burden largely on myself, with mostly 75 hour weeks (even after the other engineers were back as well). During regular hours, I did some work, but was more focused on mentorship and any tasks that were blockers. The early and late hours were when I busted out complex code.
At the engineering level, good management shows as incredibly important, especially for startups. Pressure deadlines on engineers are taxing for all - good management by top level engineers is vital for preventing burnout in everyone else, which can make it easy for people to decide to leave a company, especially when compounded by salary that does not match what the free market has to offer.