In our time working with 38 Degrees we have helped them create a lot of marketing materials designed to promote and support their campaigns and their members.
Materials were nearly always created with very short lead times, normally numbering hours not days and small budgets but none of this caused a problem. In fact the opposite can sometimes be said to be true, that in many cases when a designer is pushed by a restrictive brief it results in clever thinking and good work.*
From leaflets and posters promoting the national SAVE OUR NHS campaign, to banners for marches, graphics for petition boxes and information forms for campaigners and activists, all of the materials were created as quickly as their deadlines dictated (we need it yesterday was a typical deadline). All of this quick, responsive designing allowing them to get on with doing what they do best, managing campaigns that are powered by the UK public and make change possible.