Who says Congress isn’t an enviable gig anymore? Not the dozens of candidates running in several crowded special elections this fall.

Sure, members have historically low approval ratings and gridlock permeates the most mundane legislation. But across the country, candidates are lining up to come to Capitol Hill.

A low-profile primary Tuesday in Alabama will start a frenzy of special elections in the next couple of months — including as many as three races in one week in October. The full calendar includes a safe Democratic House seat in Massachusetts, plus two safe Republican House seats in Alabama and Louisiana. Newark Mayor Cory Booker, a Democrat, is expected to win a special election for Senate in New Jersey.

“Congressional seats don’t always come open,” said GOP consultant Guy Harrison, who was executive director of the National Republican Congressional Committee in 2010 and 2012. “These [special elections are in] areas that have been fairly well held by each party, and there are a lot of people underneath these power structures that have been interested in rising up the ladder for some period of time. So when they open up, there’s usually a lot of interest.”

Special elections are especially attractive for ambitious local pols because the barriers to entry are so low. They are shorter races, lasting only a few months compared with the slog of a typical two-year cycle. Special elections often cost less, too, and local lawmakers rarely have to give up their current offices to run in them.

It’s been a popular path to Capitol Hill for decades. Seventy-four members of this Congress first came to office via special election, including House Minority Leader Nancy Pelosi of California and 20-term Rep. Don Young, R-Alaska.

This fall’s four special-election victors will bring the group of members elected in special contests to nearly 15 percent of Congress.

Tuesday’s primary in Alabama’s deeply conservative 1st District marks the first special election on the fall calendar. The race will eventually choose a successor to former Rep. Jo Bonner, a Republican who resigned in August to take a job with the University of Alabama system.

In Alabama, candidates must receive at least 50 percent of the vote to win an election outright. But with five top-tier candidates and a handful of other Republicans running in this deep red district, it’s almost assured this race will head to a Nov. 5 runoff.

Republicans expect former state Sen. Bradley Byrne to take the first-place spot in the primary. Yellowhammer State strategists say the second runoff spot is a tossup between former Republican National Committee aide Wells Griffith, newspaper columnist Quin Hillyer, state Rep. Chad Fincher and businessman Dean Young. All four have built-in geographic bases and have raised enough money to compete.

“It’s a tight race for second place; you can flip a coin to decide who it will be,” Alabama GOP Chairman Bill Armistead said. “When you get down to it, the bottom line is whoever has the best ground game will get that second-place spot.”

No matter who makes it into the runoff, a two-person race will change the dynamics of the contests. For one, a two-person contest will allow candidates to draw clearer contrasts among a deeply conservative field. And if the field of candidates who don’t make it through the runoff coalesce their supporters around the second-place finisher, that could spell trouble for Byrne, a gubernatorial candidate in 2010.

“If you can’t hit above 45 percent when you are the most well-known guy, you just aren’t going to make that up in the runoff,” Alabama Republican strategist Bob Kish said.

Not far away in Louisiana, the race to replace former Rep. Rodney Alexander, a Republican, features similar dynamics.

The Oct. 19 special primary also has a large field, and one of the 14 candidates in a wide-open primary field must receive the 50 percent necessary to avoid a runoff. State Sen. Neil Riser is the favorite, but it’s nearly impossible for him to avoid the Nov. 16 runoff because of a crowded field.

And in Massachusetts, five Democrats are angling for the open 5th District seat on Oct. 15. This is the race to succeed Edward J. Markey, who won a Senate special election in June. It’s a wide-open contest among three candidates: state Sens. Katherine Clark and Karen Spilka and Middlesex County Sheriff Peter Koutoujian.

Democrats in that race are fighting for air time as a higher-profile Boston mayoral race takes place nearby. Democratic operatives say the race will come down to which candidate had the best ground game in what is expected to be an extremely low-turnout contest.

Finally, there’s the special election in New Jersey to succeed the late Sen. Frank R. Lautenberg, a Democrat, on Oct. 16. Booker is widely expected to defeat the GOP nominee, Steve Lonegan.

But this New Jersey race marks the first of three special elections that week, followed by House races in Louisiana and Massachusetts.

Amanda Allen contributed to this report.