The surging numbers of migrants and refugees moving through Europe have heightened the focus on the issue in Switzerland, even though the wealthy Alpine nation has yet to be significantly affected by the crisis.
The last poll from the gfs.bern polling institute showed that 48 percent of those questioned thought migration was the most important issue facing the country.
Power-sharing and consensus rule are the norm in Switzerland and elections rarely lead to major shifts in parliament or the makeup of the government, which does not directly reflect the power balance in the house.
But the latest polls suggest the scale is tilting from the centre-left towards a centre-right majority in parliament, which has 200 seats in its lower chamber and 46 in the upper chamber.
"That could clearly impact future decisions," Andreas Ladner, a political scientist at Lausanne University, told AFP, suggesting a centre-right tilt in parliament could lead to "stricter immigration policies."
About a quarter of Switzerland's eight million inhabitants are foreign nationals, and immigration and asylum policies tend to figure among voters' top concerns.
Pollster gfs.bern said the country had not seen a campaign so dominated by a single issue for decades, with only nine percent choosing the runner-up issue — Switzerland's relationship with the neighbouring European Union — as the most important.
Ties with the EU were badly hit by a narrow Swiss popular vote in February 2014 in favour of restricting immigration from the bloc.
Migration crisis boosts right
Switzerland's largest party, the populist rightwing anti-immigration Swiss People's Party (SVP), appears to be benefiting from the increased focus on its pet issue, mainly at the expense of the Greens and other smaller parties.
The latest poll handed SVP nearly 28 percent support — up from the 26.6 percent it managed in the 2011 election and close to the record high 28.9 percent it won in 2007.
"SVP is clearly benefiting from the European crisis," Ladner said.
Pascal Sciarini, a political scientist at Geneva University, however noted a heightened feeling of solidarity towards the migrants moving through Europe, which "may not benefit SVP".
He suggested the party, which in 2007 sparked outcry with posters of three white sheep kicking a black sheep off the Swiss flag, had toned down some of its anti-immigrant rhetoric.
The SVP, which championed the vote to restrict immigration from the EU, has demanded a new referendum aimed at tightening Switzerland's already strict asylum laws.
The centre-right Liberal Party, Switzerland's third largest party, holds a very different view.
The party, which has also seen a significant hike in support in the latest polls to 16.7 percent and which could help push the overall balance of parliament rightwards, stresses instead the need for more immigration to keep Switzerland's economy strong.
Lack of qualified labour
"There is no migration problem . . . the main problem facing Switzerland today is economic," Liberal parliamentarian Fathi Derder told AFP, warning the country, where unemployment stands at just over three percent, "is facing "a dire lack of qualified labour."
The Socialists, Switzerland's second largest party, which in the last poll inched up slightly from the 18.7 percent of the vote they won in 2011, also want to broaden the debate to include cleaning up the Swiss banking sector and improving ties with the EU.
Socialist vice-president Roger Nordmann warned a shift to the right in parliament could have dire consequences, especially if it hands more influence to SVP, who he accused of "playing to xenophobia".
And politicians may have a hard time convincing voters that Sunday's vote is important — with major shifts in power a rarity, Switzerland's parliamentary elections generally fail to inspire much enthusiasm and turnout has not passed 50 percent since 1975.
Moreover the Swiss can have a more direct impact in referendums held every three months on different issues as part of the country's direct democratic system.
But experts insist the stakes are high this time.
In December the new parliament will elect Switzerland's Federal Council, or government, with the seven posts traditionally shared among the major parties from right to left under a tacit decades-old agreement dubbed "the magic formula".
Despite being the largest party, SVP currently holds just one government post, but has its sights set on securing a second seat.
"One out of seven seats may not seem important, but it is in fact, since that will determine the balance of power," Sciarini said.