Firstly, it is worth noting that what we mean by "gun control" varies considerably. Most Americans are in favour of stricter gun controls, and this has been a historic trend if we're going on Gallup's polls since 1990. It's an interesting trend, since from a high of 78% of respondents saying they want stricter control in 1990, support fell to a low of 44% in 2010, and since then it has been rebounding erratically to 55% in late 2015. Those in opposition are generally in favour of the status quo rather than liberalisation of gun laws, at best only 14% of pollsters were in favour of less strict laws in 2014.
However, support for gun controls are higher when some specific questions are asked. Data from June by a CNN/ORC poll found very high support for some policies; like 92% in favour of expanded background checks, 90% in favour of those on a terror or no fly list being banned from purchasing, 87% support for a ban on felons and people with mental health issues from buying, 85% for a ban on those on a federal watch list from buying. These are the sort of proposals which recently were voted down by Congress, so for many specific gun policies there is solid support and it is not a partisan issue.
A lot less said they'd want a ban on assault weapons or high capacity clips, but it was still majority consensus at 54%. In contrast, the desire to ban guns outright is a minority opinion; only 5% of those from the aforementioned Gallup polls (a 2011 poll in this case) were for banning hand guns or bullets.
According to the same poll Democrats are decidedly more likely to vote for gun control; 78% against 29% of Republicans (and 53% of independents).
This is probably owing to the philosophical differences between the two parties. The Republican party has in recent years become the party against government; with many echoing Reagan's 1986 comment:
"The nine most terrifying words in the English language are 'I'm from
the government, and I'm here to help.'"
In comparison Democrats believe that government can be used for good, much like the phrase used in JFK's inauguration address:
"And so, my fellow Americans: ask not what your country can do for
you, ask what you can do for your country"
The crux of the schism is between classical and progressive liberalism; Republicans in the former camp and Democrats in the latter. Classical liberals view the state as an obstruction to personal liberty, as taxes and laws inhibit individual opportunities. Progressive liberals view the state as an agent promoting collective liberty; as taxes pay for public services and laws can reduce unfairness. They're attempting to tackle the same question, of how to increase liberty and prosperity, from opposite angles.
This manifests in the gun control debate, as Republicans often view gun controls as a threat to their individual rights, and Democrats often view gun controls as a means to collective security. This issue is far more emotive than usual because of what guns are; tools designed to kill people.
In the Republican view, this is primarily defensive, and gun controls remove their ability to defend themselves, which makes them feel scared. Democrats view guns as primarily offensive, and inadequate gun control as leading to increasing threats to their life, which makes them feel scared. Both sides feel highly emotional on the issue... because it invokes anxiety about death, which as you can imagine, doesn't predispose one to debate things calmly or rationally.
There's also a cultural aspect to it, as Republican strongholds are rural and southern. The right to guns in this context is seen as part of one's right to an honourable life. And that culture is lacking from most Democrat strongholds.