If the line-item veto is unconstitutional then how can...?

The line-item veto is the power of the presidency. The Supreme Court is not vetoing anything. They determine the constitutionality of an already established law, as the US Constitution charges them to do. They are charged with determining what exactly is unconstitutional with laws; an all-or-nothing approach would make the Supreme Court ineffective troubleshooters for the federal government.

The Supreme Court wasn't originally founded as an institution meant to embarrass people of political parties. It was originally meant to help lawmakers make sound law.

The severability clause which would make it possible for the supreme court to only throw out portions of the law without having to throw out the whole thing, was removed out of the bill by the dems in the house. It would therefore seem, that if part of the bill is unconstitutional, then the whole thing will be thrown out

The Supreme Courts job is to interpret what is constitutional.