Laws requiring identification at hotel check-in

I know that in many non-US countries they require identification to check into hotels. However, in the United States I am not aware of any laws that require this. Do they exist?

The reason I ask is that I have attempted to anonymously check into hotels in the United States and found it very difficult to do. For example, one conversation went this way (note that this is an in-person conversation, I am literally standing right in front of the guy at the desk with my bags):

Desk: I need a credit card and a driver's license.

Me: Why do you need to see a driver's license?

Desk: To verify the credit card.

Me: I plan to pay cash.

Desk: I still need a credit card.

Me: Why?

Desk: To guarantee your room.

Me: I will pay cash UP FRONT for the full amount of the stay plus a substantial deposit which will cover any miscellaneous charges.

Desk: I still need a credit card.

Me: Why?

Desk: I don't know, I just need it.

I have had similar conversations at several different hotels. What is going on here? Is there some secret law or something that hotels have to record your identity in the United States?

Maybe a better question would be: is it possible to check into a hotel in the United States without a driver's license and credit card?

Note I am talking about a walk-in, not making reservation. In other words just walking up to the hotel and attempting to check in, then and there, no reservation involved.

I know that in many non-US countries they require identification to check into hotels. However, in the United States I am not aware of any laws that require this. Do they exist?

Yes:

According to Massachussets legislature:

Section 27. Every innholder, and every lodging house keeper required so to do under section twenty-eight, and every person who shall conduct, control, manage or operate, directly or indirectly, any recreational camp, overnight camp or cabin, motel or manufactured housing community shall keep or cause to be kept, in permanent form, a register in which shall be recorded the true name or name in ordinary use and the residence of every person engaging or occupying a private room averaging less than four hundred square feet floor area, excepting a private dining room not containing a bed or couch, or opening into a room containing a bed or couch, for any period of the day or night in any part of the premises controlled by the licensee, together with a true and accurate record of the room assigned to such person and of the day and hour when such room is assigned.

I would imagine that legal advice has been sought by hotels and that lawyers have suggested that hotels seek official identification in order to comply with this.

In Los Angeles, an ordinance specifically targets cash or walk-in guests:

4. Renting of Hotel Rooms. The operator of a hotel shall not rent a room except in compliance with the following conditions. (a) A guest who pays all or part of the rent for a room in cash at the time of checking in, and a walk-in guest, shall be required to present an identification document or a housing voucher at the time of checking into the hoteL.

Also Tennessee has proposed a similar bill:

Hotels and Restaurants - As introduced, mandates lodging establishments maintain a guest register providing the name, address, date of birth, copy of a state or federally issued photo identification and vehicle registration information of every guest staying at the hotel; requires the hotel copy the photo ID; authorizes law enforcement personnel to inspect the registration records for law enforcement purposes.

Your next question:

I have had similar conversations at several different hotels. What is going on here? Is there some secret law or something that hotels have to record your identity in the United States?

I cannot find any evidence of any federal law regarding this and due to the other legislation found, it is unlikely that any exists that is not localised.

Maybe a better question would be: is it possible to check into a hotel in the United States without a driver's license and credit card?

I would advise you to check the booking conditions of the hotel before you attempt to check-in, for example, the hotel you list states in their FAQ (bolded text is bolded question from hotel page FAQ):

Is my ID/passport required at check in?
Yes, a valid government issued picture ID is required for Hotel Check-in.

and

What forms of payment are accepted to pay for my room?
A valid credit card is required to check in to the hotel, but guests may use cash or credit card at check-out to settle their bill.