If the 2014 election is a referendum on President Obama, Democrats are in deep trouble.

That’s according to a new state-by-state study of Obama’s job-approval ratings released by Gallup that puts his disapproval rating at over 50 percent in 10 of the 21 states where Democrats are defending Senate seats this fall. In many of those states, Republicans have recruited strong candidates and are preparing to spend big bucks to win the six seats they need to regain the majority.

Obama is deeply unpopular — with a disapproval rating higher than 55 percent — in five states: West Virginia (67.3 percent disapproval), Montana (60.9 percent), South Dakota (59.3 percent), Arkansas (57 percent) and Alaska (55.4 percent).

Beyond those five seats, there is a second tier of states where the president’s disapproval rating stands somewhere between 50 percent and 55 percent, including: Iowa (50.1 percent disapproval), New Hampshire (50.2 percent), North Carolina (50.4 percent), Colorado (51.2 percent) and Louisiana (53.9 percent).

Let’s look first at the five states where Obama’s approval rating is certain to be an issue for the Democratic candidates.

Three of those states have a Democratic incumbent retiring — West Virginia, Montana and South Dakota — and that fact, combined with Obama’s unpopularity, makes those seats tough holds for Democrats.

In Arkansas and Alaska, the Democratic incumbents are running and distancing themselves from the president as fast as they can. “Overall, I’m disappointed with the president’s State of the Union address because he was heavy on rhetoric but light on specifics about how we can move our country forward,” Sen. Mark Pryor (Ark.) said after Obama’s speech last week. Sen. Mark Begich (Alaska) offered skepticism about the president’s executive-order emphasis, disagreed with him on energy policy and said that if Obama wants to come to the Last Frontier, “I’m not really interested in campaigning” with him.

Democrats are putting considerable stock in the ability of people like Pryor and Begich — both of whom followed their fathers into elected office — to run on their own independent brands rather than be dragged down by the national one. They rightly point to North Dakota’s 2012 Senate race as a blueprint. In that campaign, former state attorney general Heidi Heitkamp, a known candidate with a well-regarded name, won despite the state’s clear Republican lean.

For his part, Begich likes to note that he won in 2008 while Obama was losing in Alaska by 22 points; the counter to that argument is that the race was wholly defined by the federal investigation surrounding then-Sen. Ted Stevens (R): The incumbent was found guilty on seven felony counts eight days before the election. There is no Stevens in this race, making it far more difficult for Begich to keep Obama (and his unpopularity) on the back burner.

Pryor didn’t even face a Republican opponent in 2008, but the Natural State has moved heavily against Obama and Democrats more broadly over the past six years, and Pryor is the last Democrat standing in Arkansas’s congressional delegation.

Of course, even if Republicans win in all five of the states where Obama is a major drag, that still leaves them a seat short of the majority. So where do they go to find that sixth seat?

Judging from the Obama disapproval numbers alone, Louisiana, where Sen. Mary Landrieu is running for a fourth term, and Colorado, where Sen. Mark Udall is seeking a second, represent the GOP’s best chances.

Landrieu has never won reelection with more than 52 percent of the vote, and because of the Pelican State’s quirky election rules, she may face a runoff against Rep. Bill Cassidy (R) in December — a contest that would immediately be turned into a national party referendum if control of the Senate were at stake.

Colorado, at the moment, looks like the GOP’s biggest recruiting failure in the nation, an opportunity lost unless the party can persuade a better candidate to run.

In two other states where Obama’s disapproval rating stands between 50 and 55 percent, Republicans have yet to coalesce behind a candidate in Iowa and continue to play a game of wait-and-see with former senator Scott Brown (R-Mass.) in New Hampshire.

And in North Carolina, Republicans are optimistic about state House Speaker Thom Tillis’s chances of surviving a primary and taking down Sen. Kay Hagan, although he remains very much an unproven statewide candidate.

Amid all of this, it’s important to remember that the Gallup numbers are from 2013 and that eight months (or so) remain before any of these Democrats will have to go before voters. It’s possible that Obama’s disapproval ratings will drop further between now and then. But even a slight comeback for the president would probably do a world of good for someone like Hagan. It’s also possible — per the Heitkamp example cited above — that people like Begich and Pryor can effectively turn the focus of their races from national concerns to state ones.

But, because Obama will never appear on a ballot again, the voters in these 10 states may decide they have only one way to express their displeasure with his leadership. If that happens, Democrats should be very worried.