A new poll has found that a small majority of Minnesotans are in favour of the decision by lawmakers to legalise equal marriage earlier this year.
Mr Dayton signed the bill into law using eight separate pens. It will allow same-sex weddings to take place from 1 August.
The poll by the Star Tribune Minnesota found that 46% of respondents were in favour of the equal marriage law, with 44% saying they were opposed. 10% said they were unsure.
Large variations are seen in gender and age differences. 57% of women supported equal marriage, compared to 34% of men. 55% of men opposed the change to the law to approve equal marriage compared to just 34% of women.
Those under 34 years old supported the change 60%, with just 41% of those over the age of 34 saying the same.
Unsurprisingly the percentage of Democrats in favour of equal marriage greatly outweighed the number of Republicans, with 78% of Democrats in favour of same-sex marriage and 18% against, and 16% of Republicans for equal marriage and 76% against.
Those with salaries over $50,000 (£32,000) were also more likely to support equal marriage, with 54% in favour, compared with only 37% for those earning less.
The Star Tribune Minnesota Poll surveyed 800 Minnesota adults June 11-13. Respondents were reached by telephone. The poll has a margin of sampling error of 3.5 percentage points, plus or minus.