Authorities are taking the lid off the alleged Nancy Guthrie ransom demand we received earlier this week … confirming they’re looking into a note that carries two deadlines.

Several law enforcement officials spoke at a press conference Thursday morning … and, while they’d previously been cagey with the public about what the note says, they’re now divulging certain details — including the first deadline, which lapses at 5 PM local time today.

The second deadline, as confirmed by authorities, is set for Monday, February 9.

They wouldn’t say what exactly changes after the deadlines hit … but — as Harvey and Charles said on “TMZ Live” — we know if the first is missed, that changes the demand … while missing the second has a more serious consequence.

As you know … Nancy went missing from her Tucson, Arizona home late Saturday night. Authorities — led by Pima County Sheriff Chris Nanos — laid out a timeline, beginning when she left for a family member’s house on Saturday evening and ending after the PCSD was called by the Guthries the next day.

Savannah has already begged for proof of life from the alleged abductors in an emotional video she posted Wednesday.

Law enforcement is still following numerous leads … including reaching out to local hospitals and pharmacies to see if they can find a place where Nancy’s captors may have gotten medication she needs, which was left behind when she was taken.