The most skilled cartographer in the world would struggle mightily right now to map out any path for Democrats to take back the House when voters go to the polls in November.

Currently, the most likely outcome appears to be Democrats picking up a single-digit net gain of seats, far from the 25 they need to retrieve the Speaker’s gavel.

“It’s going to be a modest trading session,” GOP pollster Glen Bolger said. “Republicans will pick up some Democratic seats, Democrats will pick up some Republican seats, but even with all the twists and turns, I don’t know that there’s going to be a huge shift.”

But Democrats contend that there remains the potential for a fourth consecutive wave election. “Absolutely the House is in play,” said Robby Mook, executive director of the Democratic Congressional Campaign Committee. “We’re going to pick up a large number of seats.”

However, Roll Call’s House race ratings — view our ratings chart and ratings map (PDF) — find that the Democrats’ road to net more than a single-digit gain is a steep incline.

Of the 435 House seats on the ballot, 156 are projected safe for the Democrats, compared with a projection of 195 safe seats for the Republicans. Six Republican-held seats either lean Democratic or are likely Democratic pickups. But four Democratic-held seats either lean Republican or are likely Republican pickups. That would appear to give Democrats a net gain of two.

Include new seats added through redistricting on both sides of the aisle — four Democratic, one Republican — and that probably boosts the Democrats’ net gain to six. (See Roll Call’s redistricting scorecard.)

There are 25 seats Roll Call categorizes as Tossup races. Excluding the Member-vs.-Member race in Ohio between Reps. Jim Renacci (R) and Betty Sutton (D) and a new seat in Arizona, there are 10 Democratic and 13 Republican tossups. If each category is split evenly, Democrats net about two seats.

That would lead to a net grand total of eight seats for Democrats — a long way from 25.

Still, given that there are 19 seats that lean Republican, while only 13 that lean Democratic, national Democrats see the potential for their map of real pickup opportunities to expand considerably as Election Day approaches.

Rep. Greg Walden (Ore.), deputy chairman of the National Republican Congressional Committee, said that as the map stands now, he sees November’s range falling between Democrats netting five seats and Republicans netting five seats.

Mook disagreed with that assessment. “I think they are being a little bit delusional about the strength of their own incumbents and thinking that our incumbents are weak,” he said.

Perhaps. But with the number of Democratic districts in play, a strong anti-Washington sentiment that isn’t likely to substantially favor either party and some GOP gains in 2010 solidified by decennial redistricting, it’s tough to see the Democrats’ prospects for taking back the House as anything but a long shot.

Democrats are quite likely to make gains and perhaps put themselves in a good position to flip the chamber in 2014. But the setbacks the party has faced this cycle have been significant, including in California, Florida and New York — all states where it hoped to rack up meaningful gains.

In California, GOP recruitment successes and Democratic missteps have lowered expectations for gains, once considered as high as a half-dozen seats. Democrats lost a potential pickup opportunity in the 31st district when two Republicans advanced in the June “jungle” primary, and there is little hope the party can hold the open 21st district after a series of recruitment missteps. In Florida, a court challenge to the GOP-led redistricting fell flat, leaving Democrats with a likely gain of only one to three seats, less than the six they had hoped for. And in New York, a federal judge drew a map that makes for a lot of competitive races that a Democratic gerrymander would have left comfortably in the  party’s column.

Democrats also suffered some bad breaks in the South. A new seat in South Carolina fell out of play when the only Democrat with a real shot was arrested. Three seats in Arkansas — those of retiring Rep. Mike Ross (D) and freshman GOP Reps. Rick Crawford and Tim Griffin — all appeared to be potentially competitive earlier in the cycle. Now, it looks as if a Republican will represent all of them come January.

Referring to Griffin’s 2nd district, which is anchored by Little Rock, influential Democratic pollster John Anzalone said it represented “huge missed opportunities” for his party. “The South is just not the place where you’re going to make a lot of gains this cycle,” he said.

“The South, when you lose seats like you did in 2010, it takes many, many more cycles for that to regenerate back to Democratic opportunity,” Anzalone continued. “The pendulum just swings a hell of a lot slower down there, like it’s going through the humidity.”

Of course there will be some significant Democratic victories in November, due in no small part to favorable redistricting in certain states. The DCCC is poised to do quite well in Illinois, where GOP Members such as Reps. Joe Walsh and Robert Dold are probably not coming back to Washington, D.C. Rep. Roscoe Bartlett (R-Md.) is almost certainly headed for a defeat as well.

But a snapshot of the House landscape right now shows that Democrats are poised for only modest gains.

Top Democrats believe that could change. And there are, indeed, known unknowns that could boost Democrats.

“As late as it is, it’s still early,” Mook said. “A lot of it is going to depend on big-picture factors: the president, the national environment, all those things.”

And then there are the unknown unknowns.

“When the surprises out there come,” said Anzalone, who believes there is still a chance that Democrats might take back the House, “they’re going to come in Democrats’ favor.”

Kyle Trygstad contributed to this report.