How would presidential line item veto help resolve the issue of earmarks?
In the United States, at least, a line-item veto for the president has been found unconstitutional. This means that such a veto would not be able to help resolve this issue without a constitutional amendment allowing it (or without the Supreme Court reconsidering).
If it were legal, a line-item veto would resolve the issue because it would allow the president to remove specific earmarks that were not economically useful. In Congress, such earmarks are used to "buy" the votes of specific members of Congress. Congressional budget writers have a hard time refusing to give earmarks because they might need a favor some day from the person requesting the earmark. Therefore, they give out earmarks to create political support for themselves.
In theory, the president would not need to do this. He (or someday she) would be able to veto unnecessary earmarks because he would not need to work closely with particular members of Congress in the future. This would allow the president to cut the budget in ways that Congress is unwilling to do.