Actually, according to the Constitution, we would only need 2/3 of the Members present to convict. 

Article I, Section 3, Clause 6: 

“…….And no Person shall be convicted without the Concurrence of two thirds of the Members present.”

We only need a majority present to hold a quorum. According to the Constitution, a majority is all that is required for Congress to conduct any and all business. That means only 51 members of Congress need be present at an impeachment hearing and only 2/3 of that 51 is needed to impeach.

From the SC case, United States v. Ballin (1892):

“For according to the principle of all the cases referred to, a quorum possesses all the powers of the whole body; a majority of which quorum must, of course, govern. . . . The constitutions of this State and the United States declare that a majority shall be a quorum to do business; but a majority of that quorum are sufficient to decide the most important question.”

Article I, Section 5, Clause 1:

“Each House shall be the Judge of the Elections, Returns and Qualifications of its own Members, and a Majority of each shall constitute a Quorum to do Business”

In order for Congress to conduct any and all business, 51 members of the Senate and 218 members of the House need be present. And depending on what they are voting on, either a majority of only those present or 2/3 of those present are required. Almost half of the House and the Senate could be arrested and as long as there were one member over half the total present in the quorum, they could still conduct business according to the Constitution.