I couldn't say whether the breed as a whole is "prone" to heart murmurs and cardiac related problems (take a look in OFA and you'll not find much at all in the way of reported health testing of any kind being done in comparison to the amount of Dachshunds reg'd with AKC every year - so who could say?), but for me personally I absolutely do believe that it can certainly be an issue. I believe it enough that I had my bitch OFA'd by a board certified cardiologist and will do my other when she comes of age, too.
Problem is that in this breed health testing (beyond perhaps patellas and a regular vet doing an eye exam) is not at all a given. The COE for the U.S. parent club doesn't even include any recommended testing to be done. Here in Canada we don't have a parent club but there are regional clubs across the country and none of them have any recommended heath testing in their COE's, either. So, it's up to the individual whether they feel like doing anything at all. For a Dachshund to obtain a CHIC they must have CERF and OFA Patellas, with OFA Thyroid, PRA and BAER testing being optional.