If you look at the Senate proceedings, you can see that at times the senate calls for adjournment by unanimous consent. Under this circumstance, then even one person can object and prevent the adjournment.
Friday, January 20, 2017
By unanimous consent, on the request of Mr. McConnell,
at 6:41 p.m., the Senate adjourned, under its order of today, until 3
p.m. on Monday, January 23, 2017.
On the other hand, there are cases in which a motion to adjourn is made and seconded. In that case, if the majority votes Aye, the the Senate stands adjourned. As an example here is a quote from the Senate trial of Andrew Johnson.
Mr. HOWARD. Let the vote on adjournment be announced . . . .
The CHIEF JUSTICE. Upon the question of adjournment without day the
yeas are 34 and the nays are 16. So the Senate sitting as a court of
impeachment for the trial of Andrew Johnson upon articles of
impeachment presented by the House of Representatives stands adjourned
Additionally, there is H.Con.Res.92 - Providing for a conditional adjournment of the House of Representatives and a conditional recess or adjournment of the Senate. which actually provided for the adjournment. This would mean that when the adjournment was accepted by the majority, the minority (in that session) could not object.
Resolved by the House of Representatives (the Senate concurring), That
when the House adjourns on any legislative day from Thursday, November
5, 2015, through Thursday, November 12, 2015, on a motion offered
pursuant to this concurrent resolution by its Majority Leader or his
designee, it stand adjourned until 2:00 p.m. on Monday, November 16,
2015, or until the time of any reassembly pursuant to section 2 of
this concurrent resolution, whichever occurs first; and that when the
Senate recesses or adjourns on any day from Tuesday, November 10,
2015, through Friday, November 13, 2015, on a motion offered pursuant
to this concurrent resolution by its Majority Leader or his designee,
it stand recessed or adjourned until noon on Monday, November 16,
2015, or such other time on that day as may be specified by its
Majority Leader or his designee in the motion to recess or adjourn, or
until the time of any reassembly pursuant to section 3 of this
concurrent resolution, whichever occurs first.