I would submit to you that we would never have elected a Nazi to Congress (or if we did he would have been rejected by the Congress) during WWII. The problem now is that we don't identify our enemy now as we did then. However, our enemy is having no problems identifying us.
Here's the deal, though. Suppose an elected Muslim really does try to institute Sharia law -- which would be explicitly unconstitutional. If our nation is unable to reject such moves on that basis alone, then the Constitutional foundations of the nation are rotten anyway.
The words of the Constitution are meaningless without an informed and responsible citizenry are willing to defend and live by the spirit of the Constitution. It all boils down to our real difficulty, which is that we'd rather "be nice" than do what's right.
A Muslim in Congress poses no real risk unless we're already in trouble.