With one hundred members and thousands of employees, I think it highly likely that the US Senate has enough computer work to keep at least a small staff of professionals busy full time and if it doesn't, the Congress as a whole definitely does. If political patronage is the issue, then I can't think it would be hard to extend reasonable civil service protections (under whatever name; but not necessarily the overwrought ones granted to executive branch employees) to career employees with no public policy making functions. If the existing staff isn't doing its job right, then fix that problem either by giving people the time, training, and resources needed to do their jobs; and/or replacing the people who cannot or will not perform acceptably. Then if after that, the computing staff decides that outsourcing is necessary to meet some temporary needs, then they should have the authority to make the necessary arrangements without bothering the leadership.
I see absolutely no logical reason to outsource permanent functions if there is enough work to keep someone busy full time and think it's absolutely ridiculous for government to do so; if for no other reason than that in house employees have their careers invested in the institutions that employ them, while contractors have to treat the institution as just another customer. And contractors can be even harder to fire than career civil service people, as they can afford better lawyers and are allowed to write off lobbying as a business expense.