Mocking HTTPS responses in Go

I'm trying to write tests for a package that makes requests to a web service. I'm running into issues probably due to my lack of understanding of TLS.

Currently my test looks something like this:

func TestSimple() {
    server := httptest.NewServer(http.HandlerFunc(func(w http.ResponseWriter, r *http.Request) {
        w.Header().Set("Content-Type", "application/json")
        w.WriteHeader(200)
        fmt.Fprintf(w, `{ "fake" : "json data here" }`)
    }))
    transport := &http.Transport{
        Proxy: func(req *http.Request) (*url.URL, error) {
            return url.Parse(server.URL)
        },
    }
    // Client is the type in my package that makes requests
    client := Client{
        c: http.Client{Transport: transport},
    }

    client.DoRequest() // ...
}

My package has a package variable (I'd like for it to be a constant..) for the base address of the web service to query. It is an https URL. The test server I created above is plain HTTP, no TLS.

By default, my test fails with the error "tls: first record does not look like a TLS handshake."

To get this to work, my tests change the package variable to a plain http URL instead of https before making the query.

Is there any way around this? Can I make the package variable a constant (https), and either set up a http.Transport that "downgrades" to unencrypted HTTP, or use httptest.NewTLSServer() instead?

(When I try to use NewTLSServer() I get "http: TLS handshake error from 127.0.0.1:45678: tls: oversized record received with length 20037")