Sure, that makes sense! Having a fast and slow cycle isn't a bad idea. The problem is rather that the slow cycle has too much power, and additionally uses a different electoral system from the fast cycle, so it's not just an extra brake on overly-radical mistakes, it's a potentially long-term gridlock.

If at least senate "districts" were equivalent to house "districts" (i.e. all state-based or all more regional, and both equivalently proportional), then it would be very unlikely to have long-term gridlock; instead a senate would simply serve as braking mechanism during electoral upheaval, and that's perhaps a valuable feature.