do you need to be good at math to get an economics degree?

It depends on what you mean by "good at math" and what kind of degree you have in mind.

If you have in mind something like an undergraduate degree in economics or even finance, you will be asked to use simple calculus (basically, solve static constrained optimization problems), maybe some basic linear algebra and manipulate algebraic expressions.

In *some* courses, you could be asked to demonstrate certain theoretical results. For instance, in an advanced econometrics course, I was asked to demonstrate that the IV estimator gave us an estimate of the LATE (localized treatment effect) and the question asked the derivation only for the case of a binary treatment variable. It sounds fancy, but it's just manipulating expected values, conditional expectations and knowing which hypotheses need to be made. However, before graduate courses, the bulk of what you do is applying formulas. If we are talking about finance courses, it's often even less demanding than economic courses -- they often skip over demonstrations, just give equations and formulas, jumping straight from intuition to application. I know for a fact that lots of people who study administration and mostly pick finance courses never actually perform the solution of models like the CAPM -- where I study, the underlying economic theory is learnt in a financial economics course. You usually get to do more demanding mathematics only if you bother to take math courses from the mathematics department.

Now, how hard is the above? It is a bit more demanding than high school mathematics, obviously, but until you get to a point where formal demonstrations are asked systematically, where theory is presented in very general terms, it's not harder. You just learn a procedure to solve each type of problem, just like you have been doing since 8th grade -- except even a simple general equilibrium model needs a lot more than half a page to solve!

As someone who took two courses in formal logic, I can attest of how painful rigorous formal demonstrations can get, but you won't get anywhere near this before graduate courses, most of time. From what I can tell, someone half way through his bachelor degree in mathematics is more competent at mathematics than the majority of economics PhDs. I'd actually bet that if you called all Ivy League teaching economists right now, you'll be hard-pressed to find a handful who attended about 15 or so courses of pure mathematics. I'm not sure, counting econometrics courses, if most of them had 15 courses of mathematics, applied and pure combined.

Economics look daunting because of mathematics. Then, you study it and you very quickly get to a point where it's a whole lot less impressive!

Yes,I do. But I want to major in finance or quantitative economics.