API_DOQUERY Javascript is not working

Try this and note the areas where I highlighted the code:

var promise = $.get(dbidcalendar, {
  act: "API_DoQuery",
  query: "{3.EX.178}",
  clist: "3"
});

$.when(promise).then(function(xml){
  console.dirxml(xml);
  var recordid = $("record_id_", xml).text();
  console.log(recordid);
});

or chained version:

$.get(dbidcalendar, {
  act: "API_DoQuery",
  query: "{3.EX.178}",
  clist: "3"
}).then(function(xml){
  console.dirxml(xml);
  var recordid = $("record_id_", xml).text();
  console.log(recordid);
});