What is the senate's check on the filibuster? how is this procedure invoked?

The Senate's check on a filibuster is known as a cloture. This is done by getting a vote of 3/5 of the house, approximately 60 votes. This is a rare thing to get due to number of the votes required. Rarely does one party actually have that much control. 

Cloture--with a 2/3 majority Senate vote a filibuster can be ended.

A filibuster is a long speech meant to block the vote of a bill. Both sides of Congress are able to filibuster and was used regularly starting in the 1850s. However, as the House of Representatives grew, filibustering could prevent anything from getting accomplished in Congress. The Progressive Era set to reform many government procedures and the introduction of cloture by the Wilson administration created a way around a filibuster allowing for Congress to move forward with their business if 2/3 of the chamber voted to end the filibuster.

From mexican american war , us gained new mexico.