Some say the key to overcoming the budget impasse over border security is to expand the discussion over immigration.

The political viability of that is doubtful. But if it is to occur, the mandatory use of E-Verify should come off the bench and be put into the game.

The grand bargain thinking is as follows: President Donald Trump wants funding for additional physical barriers along the southern border. Democrats want legal status for "Dreamers," those brought to this country illegally as children. Combine the two, and everyone's happy.

It is possible that Trump and enough Republicans would support such a grand bargain to pass it. But, at this point, Democrats (at least in the House) are unlikely to budge an inch on additional physical barriers at the border.

Democrats' stance on the "wall" makes no sense. Trump long ago abandoned his campaign vow to build a true wall along the complete southern border and make Mexico pay for it — although he pretends not to have.

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Republican criticism that if Democrats think that physical barriers are ineffective and immoral, then they should be arguing to take down those that currently exist, has apparently had an effect. So the Democrats' stance now is that they support the existing barriers, but oppose any additional ones.

The claim that there is precisely the right number of miles of physical barriers along the border, in precisely the right locations, isn’t credible.

But, in today's political Wonderland, support for even one more mile of any sort of physical barrier is support for Trump's wall, and therefore untouchable for a congressional Democrat.

Trump will act unilaterally

On the "wall," the path seems inevitable: Trump will invoke some presidential authority to divert already appropriated military construction dollars to build additional physical barriers. Some liberal judge somewhere will issue a national injunction against him doing that. And the Supreme Court will have to decide whether, and when, to take up the dispute.

Trump flinched on the shutdown. In the process, he made most Republicans in the Senate look foolish, voting against a temporary reopening of the government just a day before Trump accepted one.

The politics of the shutdown are unlikely to change between now and Feb. 15, when temporary funding authorization runs out. If a fifth of the federal government shuts down again, Republicans will take it on the chin. And a greater number of Senate Republicans are likely to defect if Trump wants to play wall brinksmanship again.

So, some kind of funding agreement through the remainder of this fiscal year, which ends in September, without significant funding for additional physical border barriers is likely. That battle will move to the courts.

This grand bargain is more likely to work

Does that make an expanded discussion of immigration and the search for a grand bargain a waste of time? Probably so. But there is one possibility worth at least a float.

If any funding for a wall is too toxic for Democrats, perhaps mandatory use of E-Verify won't be.

The federal government has the capability, through a digital system called E-Verify, to tell employers whether a job applicant is legally entitled to work in this country.

The system can't be gamed with made-up names or Social Security numbers. Defeating it requires identity theft, using the name and Social Security number of a real person. Such identity theft is easily detected and, if vigorously prosecuted, would be largely deterred.

Requiring all employers to use E-Verify would do far more to reduce illegal immigration than anything done at the border. It would effectively lock illegal workers out of the formal economy, the main driver of illegal immigration.

Mandatory use of E-Verify hasn't been just a Republican idea. When Arizona made it mandatory, it was signed by a Democratic governor, Janet Napolitano.

The wall and legal status for Dreamers is a grand bargain that probably isn't going anywhere. Mandatory use of E-Verify and legal status for Dreamers would be a better deal and at least somewhat more politically feasible.

Robert Robb is a columnist at The Arizona Republic, where this column first appeared. You can follow him on Twitter: @RJRobb.