The constitutionality of what they're proposing is not black and white.
Actually, it is. Extremely black and white - right and wrong. And, they are wrong, they are proposing UnConstitutional actions.
Please look at the following:
The US Constitution applies to all people within the boarders of the United States and it's possessions, not just citizens, and not just those that are not a potential threat. If a person is too dangerous to fly or requires watching by the FBI and is too dangerous to be allowed to purchase a firearm, then they are too dangerous to be allowed to walk around free, and the government should then be required to establish "Probable Cause" (as required by the 4th Amendment) before they gather any evidence but only while done under the limitations of a Search Warrant issued by a Competent Court (as protected by the 4th Amendment), then before any rights can be, violated, limited, or revoked by the government (including those of the Freedom of Movement as recognized by the Privileges and Immunities Clause of the 14th Amendment and recognized even before the 14th Amendment was enacted, by Corfield v. Coryell, 6 Fed. Cas. 546 (1823), and later by Paul v. Virginia, 75 U.S. 168 (1869), and given the fact that the power to regulate Freedom of Movement is reserved to the states by the Privileges and Immunities Clause and not a power of the Federal Government, as codified consistently through the years in cases such as Ward v. Maryland, 79 U.S. 418 (1871), the Slaughter-House Cases, 83 U.S. 36 (1873) and United States v. Harris, 106 U.S. 629 (1883)), then require the government to inform the accused of what the charges are that are being brought by the government (not some secret list that we don't even know if we've been put on it) and what evidence the accusations are based upon (as required by the 6th Amendment), then allow the accused to retain legal counsel (as required by the 6th Amendment), and allow the accused to call witnesses to testify as to their innocence (as required by the 6th Amendment) then, and only then, must the government present their case before a Grand Jury (as required by the 5th Amendment) to seek an Indictment (as required by the 5th Amendment) to ensure that the accused is provided Due Process of Law (as required by both the 5th and 14th Amendments) just as any other person being accused of a crime by the government would be afforded Equal Protection Under the Law (as required and protected by the 14th Amendment). To do less will decimate not only the rights protected by the 2nd Amendment, but the rights protected by 4th, 5th, 6th, and 14th Amendments. And could even be argued as Cruel and Unusual Punishment in violation of the 8th Amendment.
You see, it isn't that we want people on the terrorist watch list to buy guns, what we want is the government to respect and protect the fundamental rights of the people that are defined and protected by the US Constitution. These politicians took an oath to protect and defend the Constitution - that's all we're asking, for them to keep the oath they took when they were sworn into office.
It's really that simple.
If people are too dangerous to fly, then why are they not too dangerous to walk among us? Why does the mode of transportation matter when they can kill us with a bomb on the sidewalk easier than they can get one through TSA at the airport?