Actually not my rights because I have not traveled to the US yet, but yes. Disclaimer (IANAL)

The answer is has many faces - until you have entered any country you are not subject to the full jurisdiction there - Snowden was not having full rights in Moscow for the months he spent at the terminal. He was also not having full obligations - in Russia you need to register with the police as a foreigner and generally help them keep track of you when you switch your residence. So even as a US citizen while on the border you are not in the US fully.

The second is that the Supreme Court has balanced the rights and obligations of the government (the right to refuse entry and the duty to protect the country) and has determined that it is greater than the rights given by the fourth amendment.