... my transaction calls on many different inputs...
This is your basic problem.
If you compare the following two transactions:
https://blockchain.info/tx/6030f180a49391f052ad23dc21fa617c4eda4cffec0f88b2287f8a463b9f774fhttps://blockchain.info/tx/f3a513986ac4c06d57331e79e641da0d0e966c5c0ac305267285fbf679f7b8e4you'll see that the first spends lots of inputs, so the total space required in a block (and thus the blockchain) is 3680 bytes, because it needs to provide lots of different signatures to lots of different inputs.
The second, however, sends the same BTC value to the same address, but only spends a single input. As such it requires only 259 bytes of space in the block.
A miner will much prefer the second one to the first... indeed, it could fit 14 different transactions like the second one in the same amount of space in the block as the first, making it over an order of magnitude more profitable for the miner.
Both are valid, and should EVENTUALLY be included in a block... it's just that the first has a lower fee than much of the network would expect for a transaction taking up so much space, so will likely take a long time to confirm.