If Dems lose Senate in 2014, will GOP win Presidency in 2016?

[Skill and Chance]

No.  In fact, the president's party doing well in a midterm if anything makes the following presidential election tougher.  1998 and 2002 were great midterms for the incumbent party.  And the presidential elections following them both came down to one state.

Here are the cases when the president's party lost a chamber in a midterm since WWII: Truman loses both chambers in '46, wins in '48, Ike loses both chambers in '54, still wins big in '56.  Reagan arguably loses conservative control of the House in '82, wins huge in '84, Reagan loses the Senate in '86, Bush still wins in '88, Bush loses both chambers in '06, McCain loses big in '08, Obama loses the House in '10, still wins in '12.  

So 4 of the 5 times (ignoring '82) the president's party lost control of a congressional chamber in a midterm, the incumbent party won the next presidential election.  If there is any meaningful relationship, it appears to help the incumbent party win the next presidential race.  This makes some sense if the presidency is the only thing keeping the opposition from full control.  Suppose the GOP takes the senate and then Obama gets to veto ridiculous legislation nonstop for 2 years.  That likely helps the 2016 Democrat.

[Skill and Chance]

It doesn't guarantee a GOP win, but it does help in a few ways.

First, it's better for the Democrats if the party's reputation is stronger.

Obama is also more restricted with a Republican Senate which limits his ability to get the accomplishments that would raise his approval rating.

It could also force Obama to veto a lot of legislation. If Republicans are smart, they'll force him to veto legislation with broad support. Of course, Republicans can also overreach, which would result in Obama gleefully vetoing unpopular legislation that passed through party line votes. And base disappointment with a Republican led to Congress could also lead to the party nominating someone far-right.

If Republicans win Senate elections in every state Romney won, this would result in the party getting a majority in the Senate. But these states wouldn't be enough to swing a presidential election. Even wins in swing states (which Romney tended to lose) wouldn't demonstrate that the same electorate will show up in a presidential election.

You love to cite the post-WWII history of parties running for 3rd consecutive terms being handicapped.  However, the post-WWII history on congressional and presidential elections suggests just as strongly that an opposition takeover of congress in a midterm helps the incumbent president's party win the next presidential election. 

The examples are: 1946-48, 1954-56, 1986-88, 1994-96, 2006-08 and 2010-12.  We could also suggest that 1982 constitutes an opposition takeover of the House based on conservative Democrats voting with Republicans to pass Reagan's agenda in 1980-82 (although this calls into question whether a liberal Democratic majority operated in 1955-56).  So in 5/6 or 6/7 recent cases, the next presidential election was a robust incumbent party win.

[Skill and Chance]

Correction: it's actually 5 out of 7.  Republicans flipped congress in 1950 and then elected Ike in 1952.

[Skill and Chance]

You love to cite the post-WWII history of parties running for 3rd consecutive terms being handicapped.  However, the post-WWII history on congressional and presidential elections suggests just as strongly that an opposition takeover of congress in a midterm helps the incumbent president's party win the next presidential election. 

The examples are: 1946-48, 1954-56, 1986-88, 1994-96, 2006-08 and 2010-12.  We could also suggest that 1982 constitutes an opposition takeover of the House based on conservative Democrats voting with Republicans to pass Reagan's agenda in 1980-82 (although this calls into question whether a liberal Democratic majority operated in 1955-56).  So in 5/6 or 6/7 recent cases, the next presidential election was a robust incumbent party win.
[/quote]I don't think the figures suggest that losing midterm elections help a party keep the White House.

It is a small sample set consisting of six elections, four involving Presidents who would run as incumbents.
[/quote]

It may be that these numbers mean nothing.  But if we throw out the idea of an opposition congress bonus for the president's party, we also need to throw out the 3rd(+) term curse because it's based on the same small number of occurrences in the same time period: 6 of 8 candidates running to keep an incumbent party in the White House for at least 3 terms have lost since WWII, which is the same as what happens when you consider opposite party Congressional takeovers- 5 of 7 or 6 of 8 times since WWII the incumbent's party won.  Either both are relevant or neither is.