What it the longest it could take after a missed period to get pos hpt

My wife is four days late on her period. She keeps saying she feels like her body is trying to get sick. She's very week and she says she's more tired than she's ever been. The lymph nodes in her neck are swollen, and she's been having some sinus issues. A few days ago, she noticed that her cervical mucus was very thick and warm. This might be TMI, but she said there was so much that if felt like it was just going to run down her leg. It wasn't the same as the thick, creamy stuff she gets during ovulation. Also, yesterday morning, we both noticed that her boobs were a little swollen. She has taken two pregnancy tests, and they have both been negative. The last one was last night.