I used to be a Nuclear Technologist that did Stress tests. It's actually harder for people who are in shape to get their HR up. It depends on the Cardiologist, but usually they want your HR at at least 85% of max HR before injecting you with the Radioactive isotope, or, if you're doing an echo, before they take another picture of your heart. If you can't get your heart rate up, a lot of times they'll give you a medicine that will take the place of running on the treadmill.
No need to worry about the test, they monitor you the whole time, so if they see anything adverse, they know to cut it short, but the chances of that are very unlikely. Hope the test goes well and that you pass the test!