I know there is supposed be a trial in the Senate, but I'm not sure they even have to do it. I've often wondered if the mechanics of the process can be done in one day or even less time.
Under Nixon v. United States (no, not that Nixon), the Senate can do whatever it wants as long as it complies with the basic requirements set out in the Constitution, which are:
The Senate shall have the sole power to try all impeachments. When sitting for that purpose, they shall be on oath or affirmation. When the President of the United States is tried, the Chief Justice shall preside: And no person shall be convicted without the concurrence of two thirds of the members present.
Judgment in cases of impeachment shall not extend further than to removal from office, and disqualification to hold and enjoy any office of honor, trust or profit under the United States: but the party convicted shall nevertheless be liable and subject to indictment, trial, judgment and punishment, according to law.
In short: Senators have to take an "oath or affirmation," they have to let the Chief Justice preside (when trying the President specifically), they have to have a two-thirds supermajority to convict, and they can't impose penalties beyond removal and disqualification from office (but regular law enforcement can prosecute further). There is no requirement that they deliberate for any particular length of time, nor that they conduct the trial in any particular fashion. They could simply read the articles of impeachment once, and immediately vote on them.
So much for the Constitution. But the Senate is not just making things up as they go. They will follow the Senate rules when conducting a trial, which are quite extensive (document is from the 101st Congress, 1992; I don't know if a newer version exists). In principle, the Senate could change the rules by a simple majority to remove all of these procedures and convert it into an up-down vote with no actual trial. In practice, there is no chance of that happening unless the President is revealed to be a pod person from Mars.