It look a lot like a brugmansia. Although im not completely sure. Does it have any mature leaves? If it is a brugmansia the leaves will get significantly larger. Have you had it long enough to see a bloom? Without seeing a bloom it is impossible to know what variety it is, since there are hundreds of varieties. Here is my brugmansia with small leaves growing on it after losing its leaves in winter. Notice the spots/bumps on the bark and the shape of the leaves, which are also fuzzy.

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And this is the same plant while it is in bloom.
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The fact that is has the leaves oppositely arranged should help you rule out some plants (like Brugs which according to the picture above has alternately arranged leaves).

Can you tell us more about the plant, such as is it growing in a garden or the woods? Does it have any particular smell?

Otherwise, just wait a few days until the leaves are more fully open and provide a new picture.

I'm very familiar with brugs (I have one I've 'treed' growing in a pot outside my office! It's an exotic here.)

I'm in East Tennessee. No smell when the leaves are crushed. A friend at work brought it in for me to ID (I'm the 'plant lady' around here.) The leaves are very furry. They look like african violet leaves due to the hairyness, but the leaf shape is more like that of a morning glory. As you can see, there are many leaves packed into the buds.

It appears to grow in full sun or shade. The cane is thicker than my finger. Each leaf will get to be about 9 inches wide by a foot long, he tells me. The leaves stay fuzzy. He said that he went on vacation once when it was two feet tall and when he returned it was taller than the house.

With growth like that, you'd have to wonder if it is Paulownia tomentosa, Princess or Empress tree (an invasive). Did he cut it back to the ground or is it still that tall?

yes, that's it. Amazingly, this is a tree I'm quite familiar with - from a distance. They are in flower right now all over East Tennessee. I've just never been close to a budding branch of one. Very invasive pest.

Here's what I found on it:
Stem. Twigs and branches stout, glossy gray brown and speckled with numerous white dots (lenticels). No terminal bud. Lateral leaf scars raised, circular, and becoming larger, dark, and sunken. Bark light-to-dark gray, roughened, and becoming slightly fissured. Stem pith chambered or hollow and wood white.

Leaves. Opposite, heart-shaped and fuzzy hairy on both surfaces, 6 to 12 inches long and 5 to 9 inches wide. Leaves larger on resprouts, 16 to 20 inches across, with extra tips often extending at vein tips. Petioles rough hairy, 2 to 8 inches long.

Flowers. April to May. Covered with showy erect panicles of pale-violet flowers before leaves in early spring, tubular with five unequal lobes. Fragrant. Flower buds fuzzy, linear, and becoming ovoid in summer and persistent on erect stalks over winter.

Fruit and seeds. June to April. Terminal clusters of pecan-shaped capsules 1 to 2 inches long and 0.6 to 1 inch wide. Pale green in summer turning to tan in winter and eventually black and persistent into spring. Capsules splitting in half during late winter to release tiny winged seeds.

Resembles southern catalpa, Catalpa bignonioides Walt., and northern catalpa, C. speciosa (Warder) Warder ex Engelm., which have leaves with sparsely hairy upper surfaces and rough hairy lower surfaces and long slender, persistent beans.