Ogonek,

Based on your account, it appears that you are suspected of espionage. This is a very serious situation, and I think you would be well advised to get a criminal lawyer and not speak with FBI again without your lawyer present.  I am not suggesting that you should not cooperate with the FBI's investigation, but because you are a suspect, I think it would be foolish for you to do so without competent legal counsel.

The FBI cannot legally compel you to submit to a polygraph interrogation. If I were in your shoes, I would refuse. The polygraph is not a valid test to determine whether or not someone has spoken the truth. As used in criminal investigations, it is little more than a pretext for interrogating a suspect without a lawyer present: typically, no one except the polygrapher and the person being interrogated are allowed to be present in the polygraph room.

The FBI has a deliberate policy of not audio/video recording its polygraph interrogations. This gives the polygrapher a free hand to employ any interrogation tactics that he sees fit to extract an admission or confession. In the recent past, FBI polygraphers have allegedly used such inappropriate tactics as sleep deprivation, false promises, and implied threats against family members to convince suspects to sign false statements that were then used as grounds for arresting a suspect.  Examples include the interrogation of Dr. Thomas C. Butler (sleep deprivation, false promises) and Abdallah Higazy (implied threats).

You'll find more information on polygraph "testing" in AntiPolygraph.org's e-book, The Lie Behind the Lie Detector, which you can download here:

http://antipolygraph.org/lie-behind-the-lie-detector.pdf

Chapters 1-3 will be of particular interest. Chapter 1 gives an overview of the scientific status of polygraphy. As you'll see, it is sheer pseudoscience and has been roundly rejected by the scientific community. Chapter 2 includes a discussion of federal polygraph policy, including its use in espionage investigations. And Chapter 3 explains in detail the trickery on which the "test" actually depends.

See, also, the Department of Defense Polygraph Institute's Interview & Interrogation handbook for examples of the interrogation tactics you might encounter should you proceed with the polygraph:

http://antipolygraph.org/documents/dodpi-interrogation.pdf

One final point to bear in mind is that matters are further complicated by your having posted here. Members of the polygraph community read this message board, and the FBI HQ polygraph unit will no doubt be informed of your post. Based on the information you've provided, they should have little difficulty identifying you. The fact that you've posted here makes polygraphing you highly problematic. Persons being polygraphed are not supposed to know about the trickery on which the "test" secretly depends. And they're not supposed to know about polygraph countermeasures (simple techniques for passing the polygraph, information regarding which is provided in Chapter 4 of The Lie Behind the Lie Detector). But you have undeniably been exposed to such information. This is a point you may wish to discuss with your lawyer.

I do not know whether there is legal precedent for a person's refusal to submit to a polygraph interrogation being used as grounds for denying permanent residency/citizenship. I haven't heard of it happening. A person's refusal to submit to a polygraph examination is not admissible as evidence in the federal criminal courts, but I don't know if the same holds true in immigration court.

As for "black marks" on your report, it seems to me that being the subject of an espionage investigation is already a "black mark."

I suggest that you discuss your U.S. residency status, and the FBI's threat, with your lawyer.