Short version: no. If you bought (are long) a SPY call or put, you cannot be assigned. Assignment is what happens to the seller of an option when the buyer exercises. As the buyer, you hold the right to exercise — not an obligation someone can force on you.

Long vs short: who owes what

When you buy a call, you have the right to buy 100 shares at the strike. When you buy a put, the right to sell. You choose whether to use it. The person on the other side — the option writer — is the one who can be assigned and forced to deliver. So the assignment worry belongs to sellers of options and spreads, not to a long single-option scalper.

Buyers hold rights; sellers hold obligations. Assignment only flows to the side that sold.

What actually happens to your long at expiration

The real thing to manage isn't assignment — it's automatic exercise. If your long option is in-the-money at expiration and you didn't close it, the clearinghouse exercises it for you: a long call turns into a purchase of 100 shares at the strike, a long put into a sale. That can leave you holding a position (and a bill) you didn't plan for — see what happens if you can't cover it. The fix is simple: close the option before expiration instead of letting it settle.