"Senator, I've told you about all of the upside but I wanted to make you aware that the other side is claiming that the cost will be too high. Actually, this non-partisan study shows that it pays for itself over twelve months."
Now he has defused the opposing lobbyist's one-sided argument.
The business equivalent might be the act of reviewing the estimated financials of a potential investment. To show only the income would be as misleading as only showing the expenses. The informed investor wants to know both. Anyone who only gives one side loses credibility as an adviser.
A corollary tactic is to speak with the decision-maker after your weak opponent does. The idea being the weak lobbyist's one-sided pitch will be easy to knock down.
The goal is not to have the best perception possible after you're meeting, it's to have the better perception after the decision-maker walks away from the opposing lobbyist's meeting.
Only in circumstances where the opposition has no access should a lobbyist even consider this tactic. Even then, some sort of token cost-benefit discussion is needed to appear comprehensive.
President Obama's media strategy may have made this mistake in defining Mr. Romney in the worst-possible way. Since the campaign knew that Mr. Romney would have access to the electorate via paid media and public debates, it should have had a more balanced approach in order to be persuasive on Election Day. With the rise of early voting, the effects from the President's team's misstep may be mitigated since those voters presumably spent less time listening to the challenger.