It's not really as you say... Let's put it into a simpler analogy.
Let's say your uncle wants to come live with you from Iowa and he is bringing his family. He beats his wife and rapes her. He has a two sons and a younger daughter as well who are innocent in the entire conflict. You know that none of the bad things would go on under your watch, but you can only be in the home for about eight hours of the day. You don't get along with the uncle at all and he hates you because you're a Democrat, but you love his wife and kids and know they are peaceable. The wife and the kids will never testify against the uncle and they won't move in without him due to fact that they love him. Do you let the uncle move in with his family now? How about after you see that the eldest son as taken to raping the daughter after seeing how his old man treats women? Do you think you can protect the children from being turned into abusers yourself? How about if the old man threatened to kill you because of your beliefs and interfering with his ideology?
The story is fictional, but it illustrates all of the problems with radical Islam and all of the problems with what the President is doing. You think it's biased against the President when he shelters trouble elements? It's not bias, bigotry, or anything else that governs my opinions of this. The Muslims are not turning in the violent elements, and the result is we get to sit and watch as they train more violent elements. Except this time, it's in our own country instead of where they are from. Have you ever watched TV overseas and seen the anti-American commentary? Do you realize the affect local media has on American's and how much do you think it affects them?
You don't need evidence to prove what ultimately is common sense, and has already proven to never and I mean NEVER work. The Muslims coming to this country do not identify themselves as American's as a rule, and they never integrate.
I like your analogy, but don't feel like it gets as close as it could. I see it more like:
Let's say you are in a room with 14 other people and there's a door where others can enter or you can leave, but an administrator at the door checks people in and out in an official way. Out of the 15 people in the room, 3 have said one person in the room deserves to be the room's leader, 3 others have said a different person deserves to be the room's leader and the remaining 9 haven't made that determination. The 6 that think a leader is mandatory flip a coin, and now there's a leader in the room, according to the six. A few minutes later, a head count shows there are now 18 people in the room. When double checking with the administrator by the door, it is determined the 3 additional people didn't come in through the official entry way. Of the 18 people now in the room, 10 of them have no problem with the amount of people in the room, 8 of them are raising various points about the room getting crowded and perhaps we might not have enough resources. It is acknowledged that anyone who doesn't wish to be in that room are free to go, but the 8 simply concede with the idea that from now on, we might want to be sure that anyone coming into the room comes through the official entry way.
Outside of the room are a whole lot of people, and a group known as the Peace People. Some of them wish to come into the room. In fact, 2 of the members in the room are already members of the Peace People and welcome more of that group into the room. But news reports say that there's a faction of the Peace People known as Jerks who claim to be Peace People, but are really subverting that group to go along with the idea that the best way to achieve Peace is to kill all persons who are non Peace People. The leader in the room says "all Peace People are welcome in this room and are really the kind of people we wish to have here. Heck, we already have 2 of them with us now. Come on in!" The other (defeated) leader says, "Not so fast. We ought to pay attention to news about the Jerks and not just let any one claiming to be Peace People into this room. Wouldn't you agree Mr. Leader?" And the leader says, they're all Peace People. Other members in the room ask the leader about the Jerks, what he thinks about them. The Leader says, "they are all Peace People. And...." What's that, another head count shows 20 people are now in the room and administrator by the door says they didn't come in that way. Anyway, continue Mr. Leader, "....as I was saying we welcome all Peace People into the room." The 5 newest members in the room fully support the leader's rhetoric and thinks everyone ought to be welcome. Why not? Everyone is a Peace Person, right?
Another newsflash, the Jerks just killed a whole bunch more people outside of the room. Proud of their killings. Getting rid of the non Peace People. Back in the room, some members are suggesting we really ought to be keeping better track of who comes in, and right about now, it doesn't make sense to let so called Peace People into this room when anyone of them could be a Jerk who could kill us all. Heck, we're not even sure if the leader of the room believes Jerks exist. He has yet to utter them by name. So, the members ask for clarification, and if the leader is willing to allow Jerks to come in, specifically asking about Jerks. And the leader says, "They are all Peace People and ....." Newsflash, Jerks just killed many dozens outside of the room, but continue Mr. Leader, "...as I was saying, they are all welcome. How many times do I need to repeat this? We welcome all Peace People." Then someone in the room asks if the leader is a Peace Person. And the leader says, "nope, I just sympathize with the Peace People and don't want to give off the appearance of offending anyone who claims to be part of their group. You understand, right? Now, if you'll all kindly give me your guns, I think it would set the right tone when they arrive. Oh, there they are at the door. Let me go welcome them in."