In short, no. Support for stricter gun control has undergone a bumpy decline for the past few decades. This trend is depicted in the following four charts.
The first, which is taken from an article in the Huffington Post, depicts declining support for stricter gun control as documented by three major polls. The second provides more detail on the trend depicted by the Gallup poll. The third, which also uses data from Gallup, shows declining support for banning handguns over half a century. And the fourth, which uses data from an Economist/YouGov poll conducted in 2010, indicates that the share of Americans who feel closer to the Republicans on gun control is much greater than the share who feel closer to the Democrats. Interestingly, the same poll found that Americans generally feel closer to the Democrats on abortion and gay marriage, which suggests the preceding result cannot simply be attributed to a disproportionately high number of conservatives in the sample. (Credit to John Lott for finding the poll.)