How the Republicans can rescue the country without a Trump impeachment?

The Republicans will eventually realize that the threat to their Party and our country is from Donald Trump, not the Republican "base". Their "base" will simply find another shiny nut, once Trump is gone. Just like the Tea Party when they threatened to leave the Republicans but were easily coaxed back into the fold.

How do they get Trump to leave without him being impeached and convicted? That would be the ideal solution for both Parties.

There is a scenario where Trump might force McConnell's hand by assuming authority to build a "wall" on his own, in the name of "national security". If that were to happen, there is the chance that McConnell would simply bring the House bill to open up the government up for a vote. With McConnell's blessing, it would again receive almost unanimous support from both Parties.

This would force Trump's hand and he would veto the bill, in hopes that the Republicans would unite behind him, because of their "base" and their instinctual desire for survival. But, it would be a miscalculation on his part. The Senate would override his veto.

For Trump, an over-ride of his veto would be the same as an impeachment vote. He cannot tolerate such a threat over his head. He would attempt to negotiate his resignation. If that could not be negotiated, he would agree not to run for re-election in 2020.

That is a scenario for how the Republicans can get us out of this "crisis". Donald Trump has done all the good he can do for them. He is now a liability to the Party and to the country. If they can simply find a way to over-ride his veto, he will see the writing on the wall. The decision is in the hands of Mitch McConnell and the Republican Senate.