Sure, that was a concern: a sufficiently large faction of Senators might combine to protect a bad President, or destroy a good one unjustly.
> Mr. MADISON, objected to a trial of the President by the Senate, especially as he was to be impeached by the other branch of the Legislature, and for any act which might be called a misdemeanor. The President under these circumstances was made improperly dependent. He would prefer the Supreme Court for the trial of impeachments, or rather a tribunal of which that should form a part.
> Mr. PINKNEY disapproved of making the Senate the Court of impeachments, as rendering the President too dependent on the Legislature. If he opposes a favorite law, the two Houses will combine agst. him, and under the influence of heat and faction throw him out of office.
Ultimately it was decided that "in four years he can be turned out", so it was not worth addressing further. Indeed some argued that the President should not be impeachable at all because of this.
> Mr. KING expressed his apprehensions that an extreme caution in favor of liberty might enervate the Government we were forming. He wished the House to recur to the primitive axiom that the three great departments of Govts. should be separate & independent: that the Executive & Judiciary should be so as well as the Legislative: that the Executive should be so equally with the Judiciary. Would this be the case, if the Executive should be impeachable? It had been said that the Judiciary would be impeachable. But it should have been remembered at the same time that the Judiciary hold their places not for a limited time, but during good behaviour. It is necessary therefore that a forum should be established for trying misbehaviour. Was the Executive to hold his place during good behaviour? The Executive was to hold his place for a limited term like the members of the Legislature: Like them particularly the Senate whose members would continue in appointmt the same term of 6 years he would periodically be tried for his behaviour by his electors, who would continue or discontinue him in trust according to the manner in which he had discharged it. Like them therefore, he ought to be subject to no intermediate trial, by impeachment. He ought not to be impeachable unless he held his office during good behaviour, a tenure which would be most agreeable to him; provided an independent and effectual forum could be devised. But under no circumstances ought he to be impeachable by the Legislature. This would be destructive of his independence and of the principles of the Constitution. He relied on the vigor of the Executive as a great security for the public liberties.