Line-item veto for the President?

I came across this webpage on Minnesota Budget Project about a proposal in 2006 to give the President line-item veto. Although it is a bit outdated, the article makes good sense to me.

The line-item veto is the power of an executive to nullify or "cancel" specific provisions of a bill, usually budget appropriations, without vetoing the entire legislative package. This power is held by governors in all but seven US states, albeit with wide variety in its details. Presidents of the US, however, do not have this power except for a very short-period. In 1996, President Clinton was granted this power by the Line Item Veto Act, passed by Congress in order to control "pork barrel spending" that favors a particular region rather than the nation as a whole. The line-item veto power, however, was ruled unconstitutional in 1998. Since then, a constitutional amendment to give the President line item veto power has been considered periodically. This webpage in MPB talks about a recent attempt in 2006, the Gregg bill, initiated during the Bush administration.

Proponents of the bill suggested that giving the President this new authority to single out specific items in appropriations bills would force Congress to become more fiscally disciplined. However, critics pointed out that the Gregg bill had gone well beyond the traditional concept of the line-item veto in the states (such as this recent case in Minnesota) and attempted to grant the President unprecedented authority, for instance, by withholding appropriations even after a line-item veto has been defeated by the Legislature, or by bundling together line-item vetoes from separate appropriations bills in order to make it more difficult for the Legislature to override.

Critics contend that this proposal would provide the President excessive bargaining power well above political considerations [of the Congress] and consider this notion "unsupportable." It would be "an invitation to mischief" and we should find "better ways to achieve accountability" if the goal is indeed to prevent wasteful “pork barrel” spending or to reduce federal budget deficit.