[alasdair_]

A federal court issues the actual order to appear, after 2/3 of a committee or a majority of the house or senate votes to compel a witness to attend.

The witness cannot plead the fifth but they also cannot be prosecuted for anything they say.

And yes 2/3 of a committee is a small number of people.

[ncmncm]

Usually the deal is supposed to be void if they turn out to have lied or concealed relevant information.