Trade Adjustment Assistance Extension Act of 2010

Trade Adjustment Assistance Extension Act of 2010 - Amends the Trade and Globalization Adjustment Assistance Act of 2009 to extend trade adjustment assistance (TAA) programs through June 30, 2012. Extends TAA for firms and farmers through June 30, 2013.

Extends the single transition deadline for implementing certain merit-based personnel staffing requirements for state administration of TAA to a date not earlier than June 30, 2012.

Amends the Internal Revenue Code (IRC) to extend through June 30, 2012, the 80% tax credit for health insurance costs (including advance payments) for TAA (as well as Pension Benefit Guaranty Corporation [PBGC] pension) recipients.

Makes TAA recipients who are in a break in training under a training program, or who are receiving unemployment compensation, eligible for such tax credit for the period through June 30, 2012.

Amends the IRC, the Employee Retirement Income Security Act of 1974 (ERISA), and the Public Health Service Act (PHSA) to extend through June 30, 2012, the TAA pre-certification period rule disregarding any 63-day lapse in creditable health care coverage for TAA workers.

Extends the continued eligibility for the credit for qualifying family members and certain qualified TAA-eligible individuals and PBGC pension recipients for COBRA premium assistance through June 30, 2012.

Extends through June 30, 2012, coverage under an employee benefit plan funded by a voluntary employees' beneficiary association established pursuant to an order of a bankruptcy court, or by agreement with an authorized representative.

Amends the Trade Act of 1974 to expand the TAA grant program for community college and career training to include individuals who are, or are likely to become, eligible for unemployment compensation or who remain unemployed after exhausting their unemployment benefits.

Amends the Consolidated Omnibus Budget Reconciliation Act of 1985 (COBRA) to extend certain customs users fees for the processing of merchandise entered into the United States through March 31, 2020, and other specified customs users fees through April 30, 2020.

Amends the Hiring Incentives to Restore Employment Act to increase required estimated tax payments of corporations with at least $1 billion in assets in the third quarter of 2015 by 4.5% to 126.0% of such amount.