No, you read the title correct: Lindsey Graham tried to tack on an amendment to a Homeland Security funding bill that would have provided $3 billion just to be spent on border security. Yes, that Lindsay Graham, the one who said there were no votes for enforcement-only. A list of the provisions is at [1]. Now Graham says:

"Border security is the gate that you must pass through to get overall comprehensive reform."

Just part of the wranglings are further described:

Democratic leaders were scrambling after the Republican senators announced their proposal. The leadership did not want to put its members in the position of having to vote against border security. But there were parts of Graham's amendment that Democrats could not accept, such as mandatory jail time for people who crossed the border illegally after having once been deported.

At one point, Majority Leader Harry Reid offered an amendment to Graham's amendment that would have tacked on the Ag Jobs guest worker and legalization plan and the DREAM Act.

But in the end, Reid used a procedural maneuver to sideline the Republican amendment as well as his addition to it. He objected to the amendment because its provisions, he said, would be making legislative policy on a spending bill, something the Senate does not do.

The Senate voted 52-44 on that procedural vote. It would have taken 60 votes to make it possible to vote on the Republicans' measure...

Further wranglings involved Sen. John Cornyn.

UPDATE: See Lindsey Graham border security-only amendment did pass

[1] lawprofessors.typepad.com/immigration/2007/07/republicans-int.html