Mayor Martin J. Walsh holds a whopping 31-point lead over challenger Tito Jackson, with the mayor even trouncing Jackson in his home neighborhood of Roxbury, a new Emerson College poll shows.

Walsh leads City Councilor Jackson by a 52-21 percent margin, with the two other mayoral challengers, Robert Cappucci and Joseph Wiley, getting just 7 and 5 percent, respectively, according to the poll of 529 likely Boston voters.

“(Jackson) has got a tough road ahead,” said Emerson College professor Spencer Kimball, adviser to the Emerson College Polling Society, which conducted the poll from Sept. 14-16. “He’s going to make it out of the primary but then what?”

The preliminary election is set for next Tuesday.

If Jackson finishes second — setting up a one-on-one match up against Walsh — he will be a heavy underdog. The poll showed Walsh beats Jackson by a 55-26 percent margin in a general election contest, with 19 percent undecided.

The city general election is Nov. 7.

Walsh’s huge lead is bolstered by his high favorability marks, the poll shows. Seventy-two percent of voters have a favorable impression of the mayor, with just 18 percent giving him unfavorable reviews.

Jackson is viewed favorably by 43 percent of voters and unfavorably by 33 percent, according to the poll.

Walsh’s lead is consistent throughout the city — even in Roxbury, where the mayor leads by a 44-30 percent margin.

Walsh also has a 3-1 advantage (66-21) over Jackson among black voters.

The only demographic group going for Jackson is young voters. The Roxbury city councilor leads Walsh by 20 points among voters age 18 to 34.

There are some glimmers of hope for Jackson. Walsh is still polling just barely above 50 percent and 2 in 10 voters are undecided.

There is also concern among voters about development, affordable housing and crime in Boston.

More than 70 percent of voters said housing in Boston is not affordable, while 38 percent said they believed the city was overdeveloped.

Thirty-eight percent of voters also said they felt “less safe” than a year ago, compared to 30 percent who felt more safe.

Kimball said Jackson could exploit those issues, but would need Walsh’s favorable rating to drop if he hopes to win.

“Walsh would have to have some self-inflicted wounds,” Kimball said. “It would have to be that kind of perfect storm at this point.”

The Emerson poll has a margin of error of 4.2 percent.