Here is the New Mexico statute for littering. As you can see, it is a petty misdemeanor. That means it has a maximum penalty of 6 months in jail and/or a fine of up to $500. Community service -- the county will literally make you pick up litter -- can be available instead of jail time. Jail is not going to be a realistic possibility for something like this, which is good news. The bad news is that you would have a misdemeanor conviction on your record if you plead guilty to this charge.
As you are rightfully concerned with your criminal record because you are in line for a promotion at work, you should retain a criminal lawyer and let him work out something for you that will, if possible, keep you from getting a misdemeanor conviction. If you've otherwise had no difficulties with the criminal justice system, a lawyer may be able to convince the prosecutor to reduce this matter to a civil offense or to a traffic infraction. Failing that, he may be able to get you a diversion type of opportunity, where you serve a sentence consisting of fines, community service, and a brief period of supervision by probation, but when you successfully complete everything your charges are dismissed so that you don't carry them on your record.
If it's not possible for you to find a lawyer by your court date, you should plead NOT GUILTY when you are arraigned on the charges. Then you can ask the judge for a continuance to come back with your lawyer. A plea of not guilty is allowed even though you know that you did thrown the cigarette butt out of the window. It's the only plea that you can take that would allow you to work out a deal, because it's the only plea that keeps all of your rights and choices open.
The second you plead Guilty or No Contest, you are giving yourself a criminal conviction. So defendants should NEVER do that unless/until they have first worked out a deal that gets them what they want in exchange for the plea. Then they can take back their not guilty plea and plead guilty to get the promised deal.
Though this is not the world's most serious case, it has potential serious consequences for you. So have a lawyer with you on your court date and let him get you the most favorable disposition possible under the facts and circumstances of your case.