"In 1971, Congress passed a bill to rename Washington's birthday Presidents Day, and to celebrate it on the third Monday of February instead of the actual date of Washington's birth — Feb. 22. The holiday also was designated to honor Abraham Lincoln...."(emphasis added). However, if you look at the signed image of the bill to which I believe they are referring, it makes no mention of renaming the holiday or Lincoln. Further, 5 U.S.C. § 6103(a), the statute identifying "legal public holidays" continues to identify the third Monday in February as "Washington's Birthday." I can't find any mention of Lincoln. I'm open to alternative explanations though I must tentatively conclude that the story is simply incorrect as a matter of federal law. Drop a comment if you have more information!
Also, as a minor point, the Act was signed into law in 1968 although it did not take effect until 1971.
Update (2/15/2010): Jim Thomas (@jimtdenver) pointed me to his own entry (also appearing on Huffington Post) on the subject: I Cannot Tell a Lie: There is No Presidents Day Holiday. Conclusion: Washington 1; Lincoln 0.