Could a President Hillary have a Republican Congress for her entire Presidency?

[Mister Mets]

It's possible.

If Republicans run the table with the six closest races, they'll start 2015 with 54 Senate seats.

In 2016, their best pick-up opportunity is Nevada. If that goes well, Democrats would need to flip five seats to offset that.

2018 would be a midterm, which tends to be bad for the party in the White House, and also brings out an electorate more amenable to the GOP. It's likely that Republicans would pick up a few seats here.

2020 would need Hillary's coattails to be significant enough to do more than to offset the wins in 2018.

2022 is again an election in which Republicans would be favored in the Senate.

As a minor note, it's possible that Angus King will decide to join whatever party has the majority, but he'd likely join the Democrats if he determined the majority, so he doesn't count for these purposes.

[Mister Mets]

It seems that the main thing it comes down to is how many seats Republicans win in this cycle.

A few races are clustered together so the political environment that make Republicans the favorites in Colorado would probably do the same in North Carolina and Iowa.

If Clinton is a two term President, 2018 and 2022 would be years that favor the Republicans. 2016 would be a chance to undo some wins in 2010, although it doesn't seem that any of the incumbents has become a Rick Santorum. 2020 might help undo pick-ups in 2014, but those are likely to be in states that Clinton's probably not going to win (IE- Alaska, Arkansas, West Virginia, North Dakota, Montana, Louisiana) unless Republicans have a really awesome '14, which would require more incumbents to be defeated.