p.s. I just ran this in a test environment and it worked fine:
$().SPServices({
operation: "GetListItems",
async: false,
listName: "User Information List",
CAMLQuery: "<Query><Where><Eq><FieldRef Name='ID' /><Value Type='Counter'>1</Value></Eq></Where></Query>",
CAMLViewFields: "<ViewFields><FieldRef Name='LoginName' /></ViewFields>",
completefunc: function (xData, Status) {
alert(xData.responseText);
}
});