Ideally, there should be a socialist constitution in place that prevents right-wing extremist groups from wrecking the country too much (should they get elected). Also, I assume that the majority is in favor of socialism. Otherwise, the whole point of "democratic socialism" is ruined.
You mean like how India's constitution specifies that it is a "socialist republic", and yet the BJP comes to power with its communal agenda, stages riots etc?
As for the majority, the opinions of people are like waves on the sea, they always keep changing. A less charitable quote from a higher being says that "People, like sheep, tend to follow a leader - occasionally in the right direction."
I'd like to be a bit controversial here and suggest that the creation, maintenance, and propagation of socialist ideology should be the preserve of an enlightened elite. This elite will be responsible for laying the tracks down, and only then will the train move in the right direction. Without any particular track, the train will be directionless, and may even reverse direction from time to time. The progress of human civilization depends on herding the sheep in the right direction, the direction of progressive, humanist, socialist ideology, and away from religious, conservative thinking.
Inevitably, this will need some form of social control. You cannot have democratically elected socialist governments keep coming to power unless you can control what people think. This may sound a bit like "1984", but it's actually true of all governments, but more so socialist ones. You will find that in most countries with a long history of socialist rule, everything from the textbooks, the state TV stations, government policies, programs, laws etc are designed to foster socialist or progressive ideology. (The reverse is true in capitalist/right leaning countries like the US).
In the USSR for example, the government created a whole new concept of art, which is reflected in Soviet era architecture, paintings, sculptures etc. They all reflect a common theme-freedom from the capitalist yoke, working hard, hand in hand with each other to create a country for the better good of everyone. The USSR government didn't have to worry about winning elections, but about something far more important: to ensure the continued propagation of communist ideology in the people.
Democratic socialism while fine in theory, cannot exist continually in practice as long as there is democracy, and people can substitute socialism with right wing ideology.
The only way socialism can exist is through a democracy which outlaws non-socialist parties. However, even in this case, it only takes care of opinion within the country. How about outside the country? When your people look outside and see glamorous Hollywood stars, glittering super rich celebrities and illusions of "freedom", how can they manage to square that with their lives? In socialist countries, wealth distribution ensured that no one was too poor, this also meant that no one can be too rich. Guaranteed jobs, pensions and free healthcare in the Soviet model maybe don't sound too appealing to those with higher ambitions of owning global corporations, villas in Italy or diamond crusted sandals.
In conclusion, true socialism can only be achieved through a global socialist revolution. Unless each and every country in the world adheres to socialist ideology, those people in socialist countries can always be led astray by capitalist ideas. Since right wing, capitalist ideas are much easier to understand and accept, they appeal to the lowest common factor of intelligence, and vast majorities of people are usually drawn to these ideas. Socialist ideas being a bit more difficult to understand and being out of the common experience of most people, can be put in action, as I mentioned earlier, only by an intellectual elite who have a broader vision for the progress of not just their country, but of humanity.