No, there is no word missing. Breaking up the sentence should help.
Critics of the amendments fear they [i.e. the amendments] would put too much power into the hands of Immigration Minister Diane Finley. The critics also feel that by tying the amendments to the budget, the government is pushing the reforms into law without adequate debate.
In this case, the "by tying them" is referring back to the amendments.
Hope this helps.
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