Go to the technical analysis, by Edward Levine, for the point-by-point parsing. And you can see the full text of the bill itself here. But the two most obvious deal-breaker implications are:
(a) the requirement that, in order to lift sanctions, Obama must "certify" a number of extra things about Iran that are not germane to the agreement and are simply impossible to prove. For instance, Obama must demonstrate that "Iran has not directly, or through a proxy, supported, financed, planned, or otherwise carried out an act of terrorism against the United States or United States persons or property anywhere in the world," with no time limit on how far back (or forward) in time this certification is supposed to run. And:
(b) several clauses and references that apparently support the "zero enrichment" demand laid down by Benjamin Netanyahu but explicitly not endorsed by the U.S. government. These clauses, with repeated requirements that Iran "terminate" or "dismantle" its "illicit nuclear programs," are ambiguous but can (and presumably would) be read as applying to the entirety of Iran's nuclear infrastructure, peaceful or otherwise. This could mean a demand that Iran give up the right not just to weapons-grade uranium but also to low-level enrichment suitable for power plants and other non-military use.
For the background of the "zero enrichment" policy, see this 2009 paper by Matthew Bunn of Harvard's Belfer Center. He argues (as do many other people who have examined the issue) that the zero-option is theoretically appealing but in reality is completely unacceptable to Iran. Thus its inclusion in any set of "negotiating" points is a way to ensure that the negotiations fail. As Bunn puts it, "Insisting on zero will mean no agreement, leaving the world with the risks of acquiescence [to an Iranian nuclear-weapons program] or military strikes."
On the basis of logic like this, the United States and its partners have already agreed that Iran should be allowed to retain low-level enrichment capabilities. Also on this point, see The Washington Monthly, and a former Israeli intelligence chief on why low-level enrichment is reasonable for Iran. Plus President Obama's own comments at Brookings last month, on why any agreement will necessarily allow some limited enrichment. This is Obama speaking:
Now, you’ll hear arguments, including potentially from the Prime Minister [Netanyahu], that say we can’t accept any enrichment on Iranian soil. Period. Full stop. End of conversation...
One can envision an ideal world in which Iran said, we’ll destroy every element and facility and you name it, it’s all gone. I can envision a world in which Congress passed every one of my bills that I put forward. (Laughter.) I mean, there are a lot of things that I can envision that would be wonderful. (Laughter.)
But precisely because we don’t trust the nature of the Iranian regime, I think that we have to be more realistic and ask ourselves, what puts us in a strong position to assure ourselves that Iran is not having a nuclear weapon and that we are protected? What is required to accomplish that, and how does that compare to other options that we might take?
And it is my strong belief that we can envision a end state that gives us an assurance that even if they have some modest enrichment capability, it is so constrained and the inspections are so intrusive that they, as a practical matter, do not have breakout capacity.
To wrap this point up: The U.S. and its partners have already declared that they are not asking for the "zero option." That's the premise for the entire deal, and it is one that the Senate bill appears designed to reverse. It would be as if, in the middle of the SALT or START negotiations with the old Soviet Union, the Congress passed a bill requiring that any final agreement include the elimination of the full Soviet arsenal.