America obviously wasn't scared of a German/Mexican alliance because she decided to enter the war despite the telegraph's proposal. The telegraph's significance lies in the fact that the USA had a vigorous anti-war movement much of which had claimed that the Zimmermann Telegraph was a hoax devised by the British to draw the USA into the war against Germany. The inauthenticity of the telegram seemed quite plausible given the fact that it would be all but impossible for Mexico, who was in the midst of her own revolution, to retake Texas, Arizona, and New Mexico militarily given the advantages in population and mechanization that the USA possessed over her at the time. Thus the telegram's proposal looked crazy and it could easily be dismissed as a British attempt to tar the Germans as ridiculous warmongers ready to consign thousands of Mexicans to their deaths in an unwinnable war in order to divert some of the impending onslaught of doughboys away from Europe. When Arthur Zimmermann in March of 1917 admitted that the telegraph was indeed genuine then the antiwar movement in America was dealt a stiff blow because they then had to admit that the Germans were indeed crazy and/or cynical enough to propose such an action on the part of Mexico.
In the UK,school kids get told it was the Sinking of the Lusitania that brought the US into the war.
School children in the USA are also taught that the sinking of the Lusitania was a major cause for bringing the USA into the war and it certainly was, but the Zimmermann telegram was too. It should be seen as one of he greatest German diplomatic blunders in history as well as one of the greatest intelligence coups ever for the British Empire. If the Zimmermann telegram had never been sent, or never intercepted, then public opinion in the USA may never have turned against Germany enough for our elected politicians to feel secure to direct American troops to take the plunge into the bloody morass of the First World War, and Germany would have been able to end the war on much more favorable terms for herself than she did. If the Zimmermann Telegram was not a deliberate "stab in the back" by the German diplomatic corps against their own country then it was surely an inadvertent "shot in the foot".
One wonders why Zimmermann confirmed the telegram's authenticity when other German officials had been denying it. Did he do it out of an aversion to lying? That hardly seems likely in a diplomat. Did he really believe that the Mexicans would be foolish enough to attack the USA? If so then his attitude towards our Southern neighbors' intelligence was ridiculously misguided. Was he a deliberate backstabber?