It sounds nice, but congress is so powerful, going after them is nearly impossible. Which is why they openly engage in corruption.

Probably the only way to really challenge the power of congress is to expand it. For example to one congressman per 100 citizens.

The existing congress would fight this to the death, but the president could win by forming a "faux congress" within the executive branch whose debates and votes inform vetos and executive orders.

The involvement of the public would undermine the power of the de-jour congress to resist and eventually they would be supplanted.