API/BUG: Raise when int-dtype coercions fail
Related to the Index and Series constructors.

Closes #15832.

cc @ucals (since this is mostly based off what you did in #15859)
# [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=h1) Report
> Merging [#21456](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/c2da06c8eea4cc0339717aa09acdd6765bc3d673?src=pr&el=desc) will **increase** coverage by `<.01%`.
> The diff coverage is `100%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/21456/graphs/tree.svg?height=150&width=650&token=eZ4WkYLtcO&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=tree)

```diff
@@            Coverage Diff             @@
##           master   #21456      +/-   ##
==========================================
+ Coverage   91.92%   91.92%   +<.01%     
==========================================
  Files         153      153              
  Lines       49570    49586      +16     
==========================================
+ Hits        45566    45582      +16     
  Misses       4004     4004
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `90.32% <100%> (ø)` | :arrow_up: |
| #single | `41.81% <66.66%> (ø)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/indexes/base.py](https://codecov.io/gh/pandas-dev/pandas/pull/21456/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvaW5kZXhlcy9iYXNlLnB5) | `96.62% <100%> (ø)` | :arrow_up: |
| [pandas/core/dtypes/cast.py](https://codecov.io/gh/pandas-dev/pandas/pull/21456/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZHR5cGVzL2Nhc3QucHk=) | `88.49% <100%> (+0.26%)` | :arrow_up: |
| [pandas/core/series.py](https://codecov.io/gh/pandas-dev/pandas/pull/21456/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvc2VyaWVzLnB5) | `94.19% <100%> (+0.01%)` | :arrow_up: |

------

[Continue to review full report at Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=continue).
> **Legend** - [Click here to learn more](https://docs.codecov.io/docs/codecov-delta)
> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=footer). Last update [c2da06c...27caec9](https://codecov.io/gh/pandas-dev/pandas/pull/21456?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 @gfyoung if you can rebase your fixures should cleanly merge @jreback : Tests are finally green again!  PTAL. @jreback : Tests are green again.  PTAL. > perf check?

@jreback : Oh sorry, forgot to respond on that.  Perf looks good! @jreback : Comments addressed, perf looks good, and CI is green.  PTAL. thanks @gfyoung  nice patch!