Of course we know what they want: War. Tom Cotton, the Republican Senator who's been one of the leaders of opposition to any deal with Iran, has said so explicitly. He also believes that war with Iran is inevitable, so we might as well have it now rather than later, so at least his position is kinda clear. Other Republicans who aren't quite ready to come out and say "yes, let's have a war!" have more trouble explaining what they think the alternative to this deal is. What's so great about the status quo?
But here's the thing they miss and that for some reason I have seen very little mention of in the press:
We cannot get the pre-negotiation status quo back.
International sanctions against Iran have worked because they've been truly international. But Russia and China have never been particularly enthusiastic about it. They went along with the western powers because our demands seemed so reasonable: we just wanted to prod Iran into agreeing to negotiate with us about their nuclear program, to make sure they weren't going to develop a nuclear weapon. Preventing Iran from having nuclear weapons was something China and Russia could get behind, but they were never much into the broader desire of many western countries to limit Iran's power and influence more broadly.
Well, Iran did what we asked. They've agreed to a deal that was more than most people thought they would. The stated purpose of sanctions has been achieved.
If the US rejects this deal, China and Russia are going to say "if the US can't even take yes for an answer, fuck it; there's no point to these sanctions." They want to trade with Iran, and they want to sell weapons to Iran. If we accept the deal, they may hold back for a while on weapons, or limit them somewhat, but if we reject the deal, I'm pretty sure they're not going to want to have anything to do with any further international sanctions on Iran.
This process wasn't just about negotiating with Iran, it was also a negotiation with China and Russia. Accepting the deal keeps them in too. Going back to no deal means giving up the international consensus too.