Just had almost this verbatim conversation (although my automated message referred to interest rates, not debt). I spoke to them because I just applied for a new credit card and wanted to make sure it wasn't related, but when he couldn't tell me whether I was being contacted regarding a Visa or a Mastercard, or which issuer, it became convincing that this is likely a scam.
Message left: "Consumer Services we're calling in reference to your current credit card account. There's no problems currently with your account. It is urgent, however, that you contact us immediately concerning your eligibility for lowering your interest rates. Press 1 now. Your eligibility expires today. Consider this your final notice. Press 1 to be connected with a live operator."
Credit Card telemarketer. Avoid.