What book did Marmee give the girls for Christmas?

The book is never named, but from the text, we can infer it might be The Pilgrim's Progress.

"We were in the Slough of Despond tonight, and Mother came and pulled us out as Help did in the book. We ought to have our roll of directions, like Christian. What shall we do about that?" asked Jo, delighted with the fancy which lent a little romance to the very dull task of doing her duty.
"Look under your pillows Christmas morning, and you will find your guidebook," replied Mrs. March.

Note, the description of the book we are later given leads me to believe that each of the girls received a Bible, or a copy of the New Testament.

Then she remembered her mother's promise and, slipping her hand under her pillow, drew out a little crimson-covered book. She knew it very well, for it was that beautiful old story of the best life ever lived, and Jo felt that it was a true guidebook for any pilgrim going on a long journey.

"Mother wants us to read and love and mind these books, and we must begin at once. We used to be faithful about it, but since Father went away and all this war trouble unsettled us, we have neglected many things. You can do as you please, but I shall keep my book on the table here and read a little every morning as soon as I wake, for I know it will do me good and help me through the day."