As elected officials, the only requirement they can be forced to meet, is that they were elected. If you fail to give access to sensitive information to a congressman because of some problem in his getting a security clearence, then he will simply vote no when that action comes up for a vote. You can't expect people to support actions for which they are not allowed access to information on and unless someone changes the constitution, you can't make having/getting a security clearance a requirement to become an congressman.
As for the polygraph, anyone who willingly submits to one as part of a dragnet such as this, is an idiot. Polygraphs have never been proven to produce better then chance results and are not allowed as evidence in almost any court. The so called success story for the polygraph has been in intimidating believers into confessing. The test itself produces a very subjective result in the form of a graph in which many times two professional polygraphers can not even agree to what it means. Maybe they should save some money and just call the psychic hotline.
