diff --git a/pandas/plotting/_matplotlib/converter.py b/pandas/plotting/_matplotlib/converter.py
index 446350cb5d915..b2bc9b2e4abf3 100644
--- a/pandas/plotting/_matplotlib/converter.py
+++ b/pandas/plotting/_matplotlib/converter.py
@@ -264,9 +264,11 @@ def convert(values, unit, axis):
     def _convert_1d(values, unit, axis):
         def try_parse(values):
             try:
-                return _dt_to_float_ordinal(tools.to_datetime(values))
-            except Exception:
+                dtvalues = tools.to_datetime(values)
+            except (ValueError, TypeError):
                 return values
+            else:
+                return _dt_to_float_ordinal(dtvalues)
 
         if isinstance(values, (datetime, pydt.date)):
             return _dt_to_float_ordinal(values)
@@ -293,12 +295,13 @@ def try_parse(values):
 
             try:
                 values = tools.to_datetime(values)
+            except (ValueError, TypeError):
+                values = _dt_to_float_ordinal(values)
+            else:
                 if isinstance(values, Index):
                     values = _dt_to_float_ordinal(values)
                 else:
                     values = [_dt_to_float_ordinal(x) for x in values]
-            except Exception:
-                values = _dt_to_float_ordinal(values)
 
         return values
 
@@ -426,12 +429,9 @@ def __call__(self):
         ed = _from_ordinal(dates.date2num(dmax))
         all_dates = date_range(start=st, end=ed, freq=freq, tz=tz).astype(object)
 
-        try:
-            if len(all_dates) > 0:
-                locs = self.raise_if_exceeds(dates.date2num(all_dates))
-                return locs
-        except Exception:  # pragma: no cover
-            pass
+        if len(all_dates) > 0:
+            locs = self.raise_if_exceeds(dates.date2num(all_dates))
+            return locs
 
         lims = dates.date2num([dmin, dmax])
         return lims
diff --git a/pandas/plotting/_matplotlib/core.py b/pandas/plotting/_matplotlib/core.py
index 346949cb82c4d..d798db8ad290b 100644
--- a/pandas/plotting/_matplotlib/core.py
+++ b/pandas/plotting/_matplotlib/core.py
@@ -10,6 +10,7 @@
 from pandas.util._decorators import cache_readonly
 
 from pandas.core.dtypes.common import (
+    is_float,
     is_hashable,
     is_integer,
     is_iterator,
@@ -1196,10 +1197,17 @@ def _post_plot_logic(self, ax, data):
         from matplotlib.ticker import FixedLocator
 
         def get_label(i):
+            if is_float(i) and i == int(i):
+                i = int(i)
+            if not is_integer(i):
+                # TODO: is getting here indicative of a larger problem?
+                return ""
             try:
-                return pprint_thing(data.index[i])
-            except Exception:
+                val = data.index[i]
+            except IndexError:
+                # In tests we get here with both positive and negative `i`
                 return ""
+            return pprint_thing(val)
 
         if self._need_to_set_index:
             xticks = ax.get_xticks()