Actually Congress can't do squat about it. It requires a constitutional amendment.
Congress has to get the ball rolling unless the states call for a constitutional convention. But I do agree that getting 2/3 of congress and 75% of the states to ratify an amendment killing the anchor baby rule is impossible at this time.
Unless the courts change their previous precedents, this rule will stand.
Those who claim the 14th amendment automatically confers citizenship on babies born on US soil don't understand the history of the 14th amendment. For example, Native Americans were not conferred citizenship until I think the 1930s despite having been born here for many years before America existed. At the same time, the law excludes babies born to parent who are here temporarily. Since illegals are at risk of deportation, we can assume they are here temporarily too. That would mean their babies are not US citizens automatically.
IMHO, the anchor baby policy is not a matter of law, but it is more the opinions of a few liberal judges. The Supreme Court can overturn those opinions as they did with Roe v Wade. But they won't. First, there is the problem of all those anchor babies born here since a judge ruled they are citizens. Then there is the anti-Trump faction of the SC which appears to be 5 or 6 of the justices.
I am connected to my states movement to call for a constitutional convention and I can tell you it is very very slow. Blue states oppose it and those that don't want an open convention where all sorts of liberal nonsense can be introduced into the constitution. But the Convention of states wants a balanced budget amendment, term limits for congress, single issue bills in congress, the federal government out of our health care system, as well as a more clearly written 2nd amendment to end the gun grab in the US. I believe every state has a COS movement. It needs numbers to make progress. I believe Texas just joined the group of states calling for a convention by passing a resolution in the Texas legislature. That makes 19 states. We need 38,, which is a tall order.