It seems the LP vote has been relatively stable the past two or three Presidential election cycles (400K ?). What is your feeling about 2004?
Browne received about 450,000 voted in 1996, and only about 380,000 in 2004. It's hard to say this year.
Third parties don't run in a vacuum. Other third parties, the major parties, the polls, the current issues, all affect outcome.
For instance, the media and the American people seem only able to focus on one third party candidate in any election. Perot stole the limelight in 1992, got most of it in 1996, and Nader got most of it in 2000. There's no Perot this year, no Buchanan, and Nader is weaker, so that bodes well for the LP.
Third party votes are also affected by how close an election is perceived. Gore and Bush were close enough in 2000 that Nader's numbers fell several points by November, since liberals feared letting Bush win if they "wasted" their vote on Nader. If Bush and Kerry are close this year, that bodes ill for the LP.
OTOH, both Kerry and Bush are pro-war globalists (despite all the wailing of FReepers of Kerry being a "commie" and other such nonsense). There's a big anti-war block out there, if only someone will tap into it. Many will vote for Kerry because of the false perception/wild hope that he's somehow "better than Bush." Others will vote for Nader. But some may vote LP.
If the "pro-Kerry liberal media" are wise, they'll give the LP much attention, so as to siphon votes from Bush (assuming the LP gets disatisfied conservatives -- which is a debateable theory). That may help Badnarik.
In the end, how well Badnarik does depends on (1) how dissatisfied America First/fiscal conservatives are with Bush, (2) how much attention the liberal media lavishes on Badnarick, (3) how close Bush and Kerry are in November, and (4) how well/poorly goes the economy and war in Iraq.