Citizens will go to the polls on February 28th to decide on the initiative spearheaded by the Swiss People's Party, which believes that the government is too soft on foreigners who are convicted of serious crimes.
But a poll conducted for the Swiss Broadcasting Corporation (SRG) found that 49 percent of respondents would say no to the proposal, up from 42 percent from a survey conducted last month, results released on Wednesday showed.
The percentage of those favourable to the initiative fell to 46 percent from 51 percent while the share of undecided dipped slightly to five percent.
Supporters of the Swiss People's Party continue to strongly back the proposal with 90 percent of those surveyed indicating support.
A significant majority of supporters of other major parties opposed the initiative.
The survey showed that citizens of rural areas were 51 percent in favour, while only 39 percent of those living in major urban areas said they would vote “yes”.
Of the linguistic regions, Italian-speaking voters largely in the southern canton of Ticino indicated the strongest support for the initiative, with 68 percent backing it.
The proposal calls for the automatic expulsion from Switzerland of foreigners who have committed certain crimes, regardless of the seriousness of the acts or the severity of the sentence that they receive.
The federal government and parliament have rejected the proposal, warning that it would no longer allow courts to consider the particular circumstances of a case nor the personal situation involved.
Swiss voters in November 2010 backed an earlier initiative from the SVP for the expulsion of certain foreign criminals according to laws to be implemented by the parliament.
But the SVP now wants to enshrine the automatic expulsion of such criminals in the constitution.
The proposal has come under fire from human rights experts who say that it violates humanitarian law and international treaties to which Switzerland is a signatory.