diff --git a/kafka/consumer/group.py b/kafka/consumer/group.py
index c7ad0f59b..36df78326 100644
--- a/kafka/consumer/group.py
+++ b/kafka/consumer/group.py
@@ -747,7 +747,9 @@ def _poll_once(self, timer, max_records, update_offsets=True):
 
         # We do not want to be stuck blocking in poll if we are missing some positions
         # since the offset lookup may be backing off after a failure
-        poll_timeout_ms = min(timer.timeout_ms, self._coordinator.time_to_next_poll() * 1000)
+        poll_timeout_ms = timer.timeout_ms
+        if self.config['group_id'] is not None:
+            poll_timeout_ms = min(poll_timeout_ms, self._coordinator.time_to_next_poll() * 1000)
         if not has_all_fetch_positions:
             log.debug('poll: do not have all fetch positions...')
             poll_timeout_ms = min(poll_timeout_ms, self.config['retry_backoff_ms'])
diff --git a/kafka/coordinator/base.py b/kafka/coordinator/base.py
index d13ce4abb..e1d8d8336 100644
--- a/kafka/coordinator/base.py
+++ b/kafka/coordinator/base.py
@@ -1198,6 +1198,7 @@ def _run_once(self):
                     self.coordinator._lock.wait(self.coordinator.config['retry_backoff_ms'] / 1000)
 
             elif not self.coordinator.connected():
+                self.coordinator._client.maybe_connect(self.coordinator.coordinator_id)
                 self.coordinator._client._lock.release()
                 self.coordinator._lock.wait(self.coordinator.config['retry_backoff_ms'] / 1000)