You do not need excellent credit, but you can’t have bad credit either. You will need better credit if you want to apply for the Sears MasterCard issued by Citibank. This card can be used everywhere MasterCard is accepted. If your credit is not good enough for that card, they may offer you their standard store branded card.
However, if you have bad credit do not bother applying for these cards as all you will do is have another inquiry on your credit report which will lower your credit score even further. If you have bad credit there are other options. Just be sure to apply for a card designed for people with low credit scores.