Some 57 per cent of voters are in favour of tightening the asylum laws, according to a poll ahead of next month's ballot on the issue.
The government has urged voters to reject a right-wing proposal, which would limit asylum applications and cut benefits to those whose requests have been rejected.
A quarter of the 1,283 people polled said they would reject the proposal by the right-wing Swiss People's Party, with 19 per cent saying they had no opinion on the issue.
The poll, conducted before the government laid out its opposition to the initiative, comes after a similar survey last week showed that about 35 per cent of Swiss think the People's Party is the most competent to deal with the asylum issue.
On November 24, Swiss voters will decide whether to accept the party's proposal, which would prohibit asylum seekers from filing an application in Switzerland if they had passed through a so-called "safe" country first.
Since Switzerland is surrounded by "safe" countries, the effect would be to limit substantially the number of applications. The federal authorities say around 95 per cent of asylum seekers arrive in Switzerland through Austria, Italy, France or Germany.
The poll showed that a majority of voters from three of the four main parties were in favour. Some 72 per cent of People's Party members intended to vote for the initiative, with 69 and 55 per cent from their centre-right Radicals and Christian Democrats signalling their support.
Only the centre-left Social Democrats had a majority opposed - of 56 per cent - but even a quarter of their respondents said they were in favour of tightening the law.
The government says the People's Party proposal would be difficult to enforce, and would make it harder to distinguish bogus asylum claims from genuine.
"Everyone would be treated the same way," said Jean-Daniel Gerber, head of the Federal Refugee Office. "We would decide their case on the basis of whether they had entered Switzerland through a safe country and then return them there."
The poll suggests that the government is failing to convince voters that it has the asylum issue in hand - nearly three-quarters of respondents had a negative view of the situation.
Most were primarily concerned about the influx of asylum seekers, and many were worried about the cost to the taxpayer.
The strongest argument against the People's Party initiative, according to the poll, was voter concern that a tougher approach would be conflict with Switzerland's humanitarian tradition.
The poll shows some 57 per cent of voters are in favour of stricter asylum laws.
On November 24, the Swiss will vote on whether to adopt the proposed measures.
The government says the People's Party proposal would be difficult to enforce.