In Google Spreadsheet API to work on values (e.g. get, update), you can use open-ended row ranges in the form <column-start><row-start>:<column-end> (e.g. A2:A to get all cells from column A except the first row)
I want to do the same thing without specifying a column. By the way I tried <row-start>: (e.g. 2:) but it fails to parse. Also tried with a specifying the initial column <column-start><row-start>: (e.g. A2:) but same result.
I haven't found a right solution, but to simulate infinite column, you can use A:ZZZ . It seems to be the largest column range supported by the API.
So in order to get all cells starting from row 2, you can use : A2:ZZZ