Do you have a 0% APR credit card? It's pretty easy to forget when the promotional APR period ends and then you have to pay interest on whatever the balance is. That certainly hurts the case for using your credit cards this way, though the bigger issue in terms of risk is that you won't have the cash available when it's time to repay the card.
For example, you put $7,000 on a 12-month 0% APR card, paying $35/mo for the first eight months. After eight months, you lose your job. If your response is, "But that's what my emergency fund is for!" then okay, great, but you also still have to pay your regular living expenses for those four months. Your balance is still $6,720 but you also have to pay living expenses ($1,500/mo?), so once the promo period ends and you have to pay off the card in full. You'll need $12,720 in cash on hand in those last four months. I can't imagine most people have that, and the people who do probably aren't interested in making only $400-$450 in interest for that risk.
If it's an immediate cash flow issue, it makes more sense, but to just make a few hundred dollars in interest isn't worth it to me. I'm actually in this situation right now and I'm tempted to get a balance transfer card but I'd rather avoid opening another credit line just to free up cash when I can always get a 0% personal loan from First Bank of Mom & Dad.
In short, I wouldn't use a 0% interest credit card in most cases if my goal is to save money in an index fund.
I just reread your question: If the balance is already on the card and it's a 0% APR card, pay the minimum every month and put the difference in a
GSBank savings account. If it's a basic card, pay only the monthly balance. This has two primary benefits: You get 1% interest for doing nothing, and you've successfully taken a 0% loan in case you should need that cash for something, effectively giving you a temporary boost to your emergency fund. Even for a basic credit card like what you're talking about, you can average the monthly spend to get a monthly line of credit for 0% interest.