To answer your question, albeit slightly differently from what you ask, the only absolutely rigid requirements are that you ace Maths classes (Linear Algebra, Real Analysis, ODE, PDE, Mutlivariate calculus), ace the GRE (+167 in Q) and have great LORs from profs who are both familiar with your work/potential for research and can compare you to other high achieving individuals (either other people in your school who went to good schools or people they have worked with/taught in their life who went to good schools).
Now more to your actual point, you can see in the Profiles & Results threads that some people make it to top 10/20 schools with a fairly "light" background, i.e. just coursework & thesis, no RA nor TA nor masters, but those people are pretty rare, and often have very strong profiles otherwise. Profiles & Results: 2012 (Profiles and Results 2012), 2011 (Profiles and Results 2011), 2010 (Profiles and Results 2010), 2009 (Profiles and Results 2009), 2008 (Profiles and Results 2008) & 2007 (Profiles and Results 2007).
I think one piece of advice that was often given to students on this forum was to take advanced classes, i.e. grad-level classes, if you can. Either at your college or at a college nearby, to prove that you can handle graduate econ/math. A masters degree will only help, I think, if it comes from a system known to have masters that prepare you for further graduate studies: e.g. Canada, the UK, Duke, Tufts or Stony Brook (apparently). While the UK is far away, and Duke/Tufts offer limited funding, most top Canadian schools who offer MA's offer funding (Toronto Doctoral Stream MA, Queen's MA, UBC's MA) and are just on the other side of the border.
RAing seems to me like a great way to both check if you really do want to go into research in economics, and a great way to obtain great LORs. You'll be working with someone who will know your work ethic, aptitudes, capacity for innovative research (or at least generating ideas), and so on and so forth.
Now, if you do keep up your very good GPA, ace the GRE, get a masters degree from one of the universities above and are a very diligent and effective RA, I don't see what could stop you. You'll find plenty of information here. This particular thread is very useful: FAQ for Grad Students (FAQs about Graduate School in Economics and Links to Useful Threads).
To answer you in short (^^): No it's not impossible, but it would substantially enhance your application, provided you do well in either or both.