Are my romance options in ME3 limited if I cheated on my ME1 romance in ME2?
Solution 1:
While it will take effort, it will always be possible to reunite with your ME1 Romance. In that sense, 'cheating' does not limit your options in any way. However you will need to overcome an additional obstacle to your relationship.
You can also enter a relationship with either of the ME1 survivors in your squad regardless of whether you had done so previously.
Where your romance choice in ME2 does limit you is in the carryover options. Specifically, you cannot initiate a romance with any of the ME2 romantic carryovers. Unless you initiated it in ME2 (in which case it will carry over), you will be unable to enter a relationship with
Tali, Garrus, or Miranda.
Solution 2:
Definitely not. Liara is almost always available in ME3, regardless of who you cheated on her with (and I will admit that, at times, I wanted to dump Jack or Miranda or Tali to be with her). The only consequence is that sooner or later, you'll have to decide who you want to be with (if anyone), and the... breaking up part may be a little depressing. For example, if you romanced Liara in ME1, cheated on her in ME2 with the sexy Miranda, and in ME3 decided that you preferred Liara, Miranda will cry when you "break up", but will at least be understanding. The choice is entirely your to make. Note that surviving characters from ME1 can be romanced, but characters from ME2 that survived cannot be romanced in ME3 unless you romanced them in ME2.