Something worth considering if you're going to spam colonies with any race is to seed particular worlds with a full 250M colonists (or more if you can squeeze the modules in) then build a starport there and build cheap stripped-down colony ships to claim nearby worlds.
You don't need a filled colony ship to claim every new colony though. Allowing your initial colonies to grow their populations will mean that more population is available each time a colony ship is complete (by which time your scouts may have found a sweet high-PQ world that you'll want to put a full colony ship on).
If you spread so quickly that there are no prospects near to your primary colonies, you don't need to keep spamming colony ships at those shipyards - they will likely never get to a suitable site in time, and you're wasting military funding that can be better used closer to where the unowned planets are. Instead either set the shipyard to idle or build some constructors or scouts.
When your economy starts to suffer from the added maintenance from all those colonies, consider the following:
1. Do I have econ buildings queued on planets?
2. Are there so few buildings being produced that I could use Focus instead of diverting money to Social funding?
3. Do I need to spam lots of ships?
4. Do I really need that next breakthrough right now?
Rationale in reverse order:
4. Tech stagnation will happen anyway if you don't secure enough colonies for your empire, so it's not necessarily a bad thing to cut research funding while you're making a rush to the colonies. On the other hand, some techs (especially ones which unlock new improvements) are so vital that you need to get them as soon as possible.
3. During the colony rush you do need lots of colony ships, so military funding will be a priority. As soon as the colonies are grabbed, you can use Focus or 1% funding to build ships for other things like trade.
2. It's worth pointing out that it costs money to fund the construction of econ buildings. If you have too many Social projects it can choke your economy, so only build econ where you're going to break even versus the econ building maintenance. However if you only need to build a few buildings, you can use Focus on those particular colonies to divert funds away from military and research.
1. When you have econ buildings queued on planets, it's always worth keeping enough social funding so that they will be completed in good time. After all, more econ means more money which can fund anything else. On the other hand, if your needs are more pressing in another area, you can put social production on hold and then let it resume when the crisis is past.
If your particular selection of funding still has you going into the red, you can use the Production slider to scale things back. At low levels of funding, you're likely to get very little output from colonies with the production slider towards the left, so by focusing on just Military and Research, or Social and Research, or some other combination you can alleviate some of the inefficiency.
You don't pay any funding for idle shipyards (although you still pay maintenance on factories) so you can reduce the rate of your plunge into the red by cancelling production.
If you have good relations with other races you can sometimes beg them for a small amount of credits (usually 30bc). You can extort as well, in fact if you can you should do so often.