The process of impeachment and removal from office is concisely codified in the constitution and two presidents have been impeached by the house but both were acquitted by the senate. For impeachment, a house majority is required and this is possible even if the GOP controls the house. However, in order to make anything of an impeachment, two thirds of the senate have to vote for the president to be removed from office. Fat chance of that, even with a DNC senate. I don't see that ever happening.
For those who still don't know, impeachment is only the process of deciding whether to hold the president responsible for "high crimes and misdemeanors". Censure is another option that the senate may take.
I would love to see the president indicted. The constitution doesn't provide a clear answer about prosecuting a sitting president. There is no historical precedent and constitutional scholars are divided on the issue. It is theoretically possible, since it is not explicitly ruled out by the constitution but the scotus is to decide what is the intent of the document.
I can't name the clause but I think that there is a passage, something to the effect of "no one is above the law". It's in there somewhere and (if I'm right) it means that it is a constitutional principal. Principal is to be the guidance for the explication of the intent of the framers when something is not explicitly codified.
There are two arguments against it (arresting a sitting president) that are often used. Firstly, it is argued that the gov't would not be able to function smoothly and efficiently if hobbled at the highest level. Secondly, it is argued that it would be untoward for a grand jury to undo the will of the people as expressed by an election. I'm sure that there are other arguments and I'd love to argue them.
To the first, I would not even respond. It's irrelevant. The agenda of a criminal should not be the agenda of the gov't and such a regime should be hobbled. To the second, I actually find it to be a strong constitutional argument. I did not say that I concede to it. In this case we are investigating the collusion of the regime with a foreign government having interfered in that very election.
“It is proper, constitutional, and legal for a federal grand jury to indict a sitting president for serious criminal acts that are not part of, and are contrary to, the president’s official duties. In this country, no one, even President Clinton, is above the law." -Ken Starr