Kangaroos are basically (for a broad definition of "basically") just upright deer. Indeed, a side-by-side comparison of the eastern grey kangaroo and the ubiquitous white-tailed deer suggests they share much the same ecological niche:
- They are ruminants with similar diets, mainly consisting of grass and low-lying plants of various descriptions. Deer in the eastern US mostly consume scrub and brush because that's what's most available, but in the west they're perfectly happy to graze on grasses. Conversely grey kangaroos are mostly grass-eaters but there are other species of kangaroo that prefer brush.
- They have broadly similar social habits, revolving around small family units. Kangaroos are more inclined to former larger groups, in the ~10 member range, though this appears to vary with geography.
- Their natural predators are similar... to an extent. Coyotes and dingos are very much akin to one another, being predatory canids of about the same size. However, North American predators can get quite a bit bigger than (extant) Australian ones. In the western part of the continent, kangaroos would have to contend with wolves and bears, but in the east they are less common.
- Their interactions with humans are similar. They are relatively skittish and typically pose no threat to humans (except on roadways, where they are both menaces to careless drivers).
- What kangaroos have, and deer lack, are a wide variety of coping mechanisms for extreme aridity that will virtually never be useful in the eastern US. (They might find some use for it in the west, but never to the same extent as in the Outback.) This suggests that they would be outperformed by native species until they manage to adapt. Wikipedia suggests they require a particular habitat to reproduce but doesn't say what; if this is taken to mean that they need access to the covered part of their range (with trees and brush) as opposed to the open grassland then they're fine. If their needs are more specific, it could be a problem.
- Conversely, kangaroos are probably less adept at surviving winter. They can readily survive temperatures down to the single digits Celsius, but rarely have to encounter multiple months below freezing as occurs in the northern part of their proposed range. They might fare better in the south.
- As for how fast they can grow: in theory, very fast. Finland has a population of about a hundred thousand deer descended from a handful of animals shipped over in the mid-30s, meaning a tenfold increase in population every 20 years or so. Your kangaroos will probably not be so fortunate, because of the different climate than what they're used to, but if they thrive in North America they could grow quite rapidly.
Tl;dr: the main problems would be adapting to a wetter, colder environment and potentially large predators such as bears. Their main competition would be medium-sized grazers like deer, and their main predators would be coyotes and the like.