WASHINGTON — One overarching law is almost always applicable in Washington — the law of unintended consequences.

Time and again, Congress takes steps to fix a problem, only to end up further aggravating the situation or creating a whole new issue. Such is the case with the National Emergencies Act of 1976, enacted in the post-Watergate era to rein in presidential power. It has instead provided President Trump with a route to expand executive authority — in defiance of Congress — by declaring a national emergency to fund a wall along the southwestern border.

On Friday, the president issued his first veto after Congress rejected that declaration.

Now, with the immediate partisan fight over Mr. Trump’s border emergency diminishing, those in favor of overhauling the 1976 law he invoked remain determined to pursue bipartisan changes in legislation they view as an abject surrender of congressional power.

“Ultimately, this is a problem created by Congress, and it has been allowed to persist by Congress,” said Senator Mike Lee, Republican of Utah, who introduced a measure this past week to make it more difficult for presidents to circumvent Congress through an emergency declaration. “Congress is starting to wake up to the fact that over time it has delegated out too much power.”