How bad is early game mass debt?

Going into mass debt (running your mass down to zero and staying there) in the early game is bad if you are building more than one project at a time; especially if that one project is not a mass extractor (either build or upgrade) that will help solve future mass debt problems. This is because trying to build multiple projects while in mass debt slows all of the projects due to the lack of mass to finish them.

It is far better to finish one project and then start the next one, rather than stall a bunch of projects by trying to complete them all at the same time. Nothing is sadder than an unfinished project. Unfinished projects do nothing for you. A half-finished mass extractor doesn't give you mass, a half finished power generator doesn't give you power, and an unfinished tank in your factory certainly won't protect your base.

If you anticipate going into mass debt, it is best to start fewer projects, and if possible, make the highest priority project one that will help you produce more mass, such as building or upgrading your mass extractors.

To answer your question directly, in the early game if you have more than one engineer and are mass starved, ask yourself: did I need to build some of those engineers? Maybe I should have put their mass into upgrading my mass extractors instead. I would have fewer engineers but produce more mass. Maybe I could actually have all my engineers working at the same time if I had more mass and fewer engineers. Remember; an idle engineer a sad thing, he is a waste of the mass and time he took to produce. At the very least send out idle engineers to reclaim rocks and trees.

Playing Supreme Commander well is all about balance. You are balancing four things:

1) mass production: building and upgrading mass extractors, reclaiming rocks and dead units.
     Low mass production results in continual mass debt, and projects that complete slower.
     Too much production results in a full mass storage bar. Never waste mass this way.

2) power production: building power structures, reclaiming trees.
     Low production results in power debt, and your shields/radar will shut down.
     Too much production results in a power bar that is always full.
     You never want your power bar to go to zero, but it should fluctuate from full.

3) Building ability: building more engineers and factories.
     Low production results in a waste of mass when your mass storage fill up.
     Too much production (too many engineers and factories) results in
         either idle engineers or factories, or mass debt when you use them all.
     Idle engineers can be sent to reclaim rocks, trees, or killed/dead units. 

4) military power: building military units and structures.
     Low production results in your base being overrun.
     Too much production weakens your economy. Which is ok if you are just before winning.
     If you have too many military units, send an attack to ruin your opponent's economy!

An unbalanced economy means you have put too much effort into one part of your economy, resulting in too little production in another. You want to build just enough of all of them to have the most efficient economy possible, which is defined as one that grows as fast as possible. The side with the biggest economy is able to build a bigger army, and build it faster than their opponent can.

When you watch a "lets-play" video of really good players, or even better an analysis of someone's game, pay attention not only to what they are doing in the game but also to their resource (mass and power) storage bars at the top of the screen while they play. Notice that their resource bars meters are never at zero, but they are always very close to zero. They are using up their mass and energy as fast as they produce it. This is the ideal you should strive for.

So knowing all this, while playing, continually ask yourself:

 will I soon run out of power? (build more power generators).
 Will I soon run out of mass? (build or upgrade mass extractors).
 Is my mass bar getting almost full? (Start some mass hungry projects or
           build more engineers to work on current projects).
 Will I soon be overrun? (build more military units).

Whichever of these will be your biggest upcoming problem tells you which aspect of your economy you need to prioritize next. When you play a game and lose, notice how your economy was weak. Were you always in mass debt? Did you run out of power? In your next game change what and when you build things to adjust for that problem. You should turn on the economy display in your game if you are unsure of where your resources are going; this display will show you how much mass and/or energy each of your units and buildings either produce or consume.

Energy and mass storage structures are a special subsection of your economy. While they do help your economy a little if built in the correct locations (adjacent to appropriate buildings), their real effect to your gameplay is to give you more time to react to problems in your economy. If you are running out of power while in battle, you must do something about it immediately before your lack of power drops your shields and radar. You must react to this problem even if it means abandoning your military units to make their own decisions during the battle. If you have some energy storage structures you may be able to wait until the battle is over, which means you can micromanage the battle (allowing you to win it better) and only then tweaking your economy to fix the energy problem after the battle is over.

One trick I use later in the game to keep from having either a full or empty mass storage bar is to create a really big project like an experimental as an excess mass absorber. I then add engineers to that project when my mass storage gets too full, and pull engineers off to do other things when my mass gets low. Of course, if you are playing in a team, you could always gift your teammates with that mass, since they will probably need it for something.