How to Get to Mr. House's Chamber in Fallout: New Vegas

Acquire heavy armor. Power armor works best.

Get a good heavy weapon. Make sure it is relatively easy to use, like a mini-gun, rocket launcher, or Gatling laser. Alternatively, you can use a Pulse Gun (your main enemies are robots).

Gather a full party (two companions). Preferable options would be Veronica or Lily.

Travel to New Vegas. Go inside the Lucky 38.

Use the elevator to the top floor. Go to the room you find Mr. House's monitor.

Go left. You should find another room. Find the terminal located on the wall.

Walk along the wall until you find the hidden door. Mentally mark its position, then go back to the terminal.

Open the terminal, then activate the door. Confirm the order.

Wait for the door to open, then take out the sentries on the other side of it. Do not worry about the ones behind you.

Run. Do not take off your armor; you will need protection more than agility. Race for the terminal in the other room.

Open the terminal, then enable access to the private elevator. Open the elevator.

You are now inside Mr. House's chamber. You can open the cryo-storage to rid him of access to the sentries, or assassinate him.