diff --git a/doc/source/whatsnew/v2.0.0.rst b/doc/source/whatsnew/v2.0.0.rst
index a30d68319cafe..b9ee5d5590861 100644
--- a/doc/source/whatsnew/v2.0.0.rst
+++ b/doc/source/whatsnew/v2.0.0.rst
@@ -630,6 +630,7 @@ Other API changes
 Deprecations
 ~~~~~~~~~~~~
 - Deprecated argument ``infer_datetime_format`` in :func:`to_datetime` and :func:`read_csv`, as a strict version of it is now the default (:issue:`48621`)
+- Deprecated behavior of :func:`to_datetime` with ``unit`` when parsing strings, in a future version these will be parsed as datetimes (matching unit-less behavior) instead of cast to floats. To retain the old behavior, cast strings to numeric types before calling :func:`to_datetime` (:issue:`50735`)
 - Deprecated :func:`pandas.io.sql.execute` (:issue:`50185`)
 - :meth:`Index.is_boolean` has been deprecated. Use :func:`pandas.api.types.is_bool_dtype` instead (:issue:`50042`)
 - :meth:`Index.is_integer` has been deprecated. Use :func:`pandas.api.types.is_integer_dtype` instead (:issue:`50042`)
@@ -637,6 +638,7 @@ Deprecations
 - :meth:`Index.holds_integer` has been deprecated. Use :func:`pandas.api.types.infer_dtype` instead (:issue:`50243`)
 - :meth:`Index.is_categorical` has been deprecated. Use :func:`pandas.api.types.is_categorical_dtype` instead (:issue:`50042`)
 - :meth:`Index.is_interval` has been deprecated. Use :func:`pandas.api.types.is_intterval_dtype` instead (:issue:`50042`)
+-
 
 .. ---------------------------------------------------------------------------
 .. _whatsnew_200.prior_deprecations:
diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index 2d31eeaa53a61..9d9b93f274c60 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -1,3 +1,7 @@
+import warnings
+
+from pandas.util._exceptions import find_stack_level
+
 cimport cython
 
 from datetime import timezone
@@ -303,6 +307,16 @@ def array_with_unit_to_datetime(
                         raise ValueError(
                             f"non convertible value {val} with the unit '{unit}'"
                         )
+                    warnings.warn(
+                        "The behavior of 'to_datetime' with 'unit' when parsing "
+                        "strings is deprecated. In a future version, strings will "
+                        "be parsed as datetime strings, matching the behavior "
+                        "without a 'unit'. To retain the old behavior, explicitly "
+                        "cast ints or floats to numeric type before calling "
+                        "to_datetime.",
+                        FutureWarning,
+                        stacklevel=find_stack_level(),
+                    )
 
                     iresult[i] = cast_from_unit(fval, unit)
 
diff --git a/pandas/io/json/_json.py b/pandas/io/json/_json.py
index afb0be0729344..fb64e089d53a8 100644
--- a/pandas/io/json/_json.py
+++ b/pandas/io/json/_json.py
@@ -1222,7 +1222,9 @@ def _try_convert_to_date(self, data):
         if new_data.dtype == "object":
             try:
                 new_data = data.astype("int64")
-            except (TypeError, ValueError, OverflowError):
+            except OverflowError:
+                return data, False
+            except (TypeError, ValueError):
                 pass
 
         # ignore numbers that are out of range
diff --git a/pandas/tests/groupby/test_value_counts.py b/pandas/tests/groupby/test_value_counts.py
index 3d1228d65ac7c..ae4b74fc814da 100644
--- a/pandas/tests/groupby/test_value_counts.py
+++ b/pandas/tests/groupby/test_value_counts.py
@@ -135,9 +135,7 @@ def test_series_groupby_value_counts_with_grouper(utc):
         }
     ).drop([3])
 
-    df["Datetime"] = to_datetime(
-        df["Timestamp"].apply(lambda t: str(t)), utc=utc, unit="s"
-    )
+    df["Datetime"] = to_datetime(df["Timestamp"], utc=utc, unit="s")
     dfg = df.groupby(Grouper(freq="1D", key="Datetime"))
 
     # have to sort on index because of unstable sort on values xref GH9212
@@ -1010,9 +1008,7 @@ def test_value_counts_time_grouper(utc):
         }
     ).drop([3])
 
-    df["Datetime"] = to_datetime(
-        df["Timestamp"].apply(lambda t: str(t)), utc=utc, unit="s"
-    )
+    df["Datetime"] = to_datetime(df["Timestamp"], utc=utc, unit="s")
     gb = df.groupby(Grouper(freq="1D", key="Datetime"))
     result = gb.value_counts()
     dates = to_datetime(
diff --git a/pandas/tests/tools/test_to_datetime.py b/pandas/tests/tools/test_to_datetime.py
index dfbe78e53de40..a1217b268613a 100644
--- a/pandas/tests/tools/test_to_datetime.py
+++ b/pandas/tests/tools/test_to_datetime.py
@@ -1723,11 +1723,13 @@ def test_to_datetime_month_or_year_unit_non_round_float(self, cache, unit):
         # GH#50301
         # Match Timestamp behavior in disallowing non-round floats with
         #  Y or M unit
+        warn_msg = "strings will be parsed as datetime strings"
         msg = f"Conversion of non-round float with unit={unit} is ambiguous"
         with pytest.raises(ValueError, match=msg):
             to_datetime([1.5], unit=unit, errors="raise")
         with pytest.raises(ValueError, match=msg):
-            to_datetime(["1.5"], unit=unit, errors="raise")
+            with tm.assert_produces_warning(FutureWarning, match=warn_msg):
+                to_datetime(["1.5"], unit=unit, errors="raise")
 
         # with errors="ignore" we also end up raising within the Timestamp
         #  constructor; this may not be ideal
@@ -1742,7 +1744,8 @@ def test_to_datetime_month_or_year_unit_non_round_float(self, cache, unit):
         expected = Index([NaT], dtype="M8[ns]")
         tm.assert_index_equal(res, expected)
 
-        res = to_datetime(["1.5"], unit=unit, errors="coerce")
+        with tm.assert_produces_warning(FutureWarning, match=warn_msg):
+            res = to_datetime(["1.5"], unit=unit, errors="coerce")
         tm.assert_index_equal(res, expected)
 
         # round floats are OK