Interaction of charged triphosphates with the ATP binding region in proteins
Summary
Many proteins that bind the nucleotide triphosphates ATP and GTP have an evolutionary conserved motif — the P-loop — that binds the phosphate portion of the molecule. This has the sequence, GXXXXGKS/T. Although the conserved basic lysine (K) is interacts with two of the positively charged phosphate moieties, other interactions involve Mg2+ ions (with which NTPs are always complexed) and polar, rather than charged, amino acid residues and the polypeptide backbone.
Detailed Illustration
Although the question asks about ATP, I have chosen the GTP-binding protein H-ras p21 as an illustration because the paper by Pai et al. describing it gives full details of the interactions of the phosphates, which are essentially the same for ATP and GTP. (Many other papers tend to show only ribbon diagrams of the protein.) Note also that the crystal structure was, of necessity, of a complex with the GTP analogue, GppNp. (GppNp is not rapidly hydrolysed, unlike GTP itself.)
In this case the evolutionary conserved P-loop that binds the phosphate has the sequence:
Gly Ala Gly Gly Val Gly Lys Ser

 10  11  12  13  14  15  16  17

A three-dimensional representation of the phosphate-binding region is shown below. The left-hand frame shows the P-loop and residues Thr35 and Asp57 without the nucleotide. The right-hand frame is the same but with GppNp and a magnesium ion included, and only the conserved residues of the P-loop labelled.

[Own work based on Fig.6 of the paper by Pai et al. using Jmol software and Protein Data Bank file 5p21.pdb.]
A two-dimensional schematic of the interactions is shown below. The side-chain interactions (and those from the magnesium ion) are shown as red dotted lines, whereas those from the backbone are shown in black. The conserved residues of the P-loop are indicated by blue text.

[Simplified redrawing of part of Fig.5 of the paper by Pai et al., excluding water interactions and interatomic distances.]
Reflections
Although positively-charged basic amino acid side-chains are involved in neutralizing the negative charges of nucleic acids and nucleotide phosphates, they are not the sole means of doing so, and in the case of the NTPs they are not the main means. Magnesium ions and polar residues (including the protein backbone δ+ve NH groups) can play an important role. To my mind this reflects two things. First, that life is dynamic; so weaker interactions are often favoured in enzymes because they can be easily broken as well as made. (NDP must be released from the enzyme after hydrolysis.) Second, and more speculative, the P-loop is thought to be very ancient as it is found in a wide variety of conserved NTP-binding proteins. A specific backbone conformation has been identified that facilitates this interaction. It could have arisen before all 20(ish) proteins specified by the genetic code had arisen, when the protein backbone could have played a greater role in interacting with small molecules. (This has also been suggested for backbone NH groups binding δ+ve sulphur in iron–sulphur clusters.)