Nine women can't produce a baby in a month
There is some useful theory on this subject. A number of writers in the 1980s published algorithms to help estimate project duration and team size, based on the observation of many software projects. You can read more about this subject in books such as "Controlling Software Projects"by Tom deMarco, Software Engineering Economics by Barry Boehm and Measures for Excellence by Putnam and Myers. However these sources agree that the evidence is that in order to bring a project end-date forward you need to deploy exponentially more resources to do that. The theory actually shows an equation relating the elapsed time to effort as:
effort = constant/time to the power four
which for the less mathematically inclined means that the end date (project time) has a BIG effect on the effort needed. For example a project that was estimated at 18 months elapsed (a nice round number selected by IT management) could, if it was extended to 19 months, be done with 20% less effort. That's right: by extending your elapsed time by 5% you need 20% less effort. When I first saw this it seemed almost absurd, until I got involved briefly in project estimating when I worked at Shell and observed two projects in the upstream. They were that rare thing: the same project, but being done in different Shell subsidiaries. They were independent, and were the same size and scope. One project was estimated to 13 months, the other was to take the same, but in one project a decision was taken to bring forward the elapsed time to 12 months in order to fit in with another project. Money was not a major factor on this particular project, and more resource was piled in to bring the date forward. Remarkably, the compressed project took 50% more effort to bring in than the one which ran its "natural" course, something that caused general bewilderment at the time but one which actually fits in tolerably well with the software equation above.
Why is the effect so dramatic? By adding new people to a project, people that were working on the project have to stop what they were doing an on-board the new people. Now there is a bigger team, the communication becomes trickier, as more people need to be involved and the project specification is open to interpretation by more people. As you add more and more people the problem worsens: now people don't fit into one room any more, so they have to have a meeting in order to solve a problem rather than just turning to their neighbor etc.
The message is that if you have a project that is having problems with its schedule, it is much easier to reduce the scope of the project slightly, and deliver the rest of the functionality in a later phase, than it is to try and pile on more resources to cram it into the original schedule. If you can't reduce the scope of the project then you can only make the people on project more productive (good luck with that) or add a LOT of resources. At least there is a formula you can look up to tell you many more resources you need, even if management won't like the answer.