In addition to not having budgets for programmers, we also don't know how to manage them, for instance how to communicate our needs, decide if their implementation plans make sense, or gauge their progress. Nearly half a century after The Mythical Man Month, managing software development is still generally acknowledged to be an unsolved problem.
The other two obstacles are that most programmers hate the scientific work environment, with its ever-changing requirements and frequent dead ends. And, the programmers who can work on math related stuff are in the highest demand.