The Texas Equal Suffrage Association, the state chapter of the National American Woman Suffrage Association, adopted its constitution at a convention in Houston in December 1903. No statewide group promoting woman suffrage had been active since 1895, when TESA's predecessor, the Texas Equal Rights Association, ceased functioning. The establishment of TESA, originally named the Texas Woman Suffrage Association, was due largely to the energy and persistence of Annette Finnigan of Houston, who had organized a local suffrage league in that city and who was elected president of TESA in 1903. Only Galveston and Houston suffrage clubs sent representatives to the founding convention. Finnigan ascribed the group's sluggish growth over the next several years to the size of the state and the sparseness of its population, which made organizing local chapters arduous and expensive. When she moved out of state in 1905, TESA became inactive. With the exception of a suffrage group established in Austin in 1908, the cause of woman suffrage languished for about six years, but a statewide tour by NAWSA president Dr. Anna Howard Shaw in 1912 revived interest. Finnigan was again a key figure, having returned to the state and reorganized the Houston Suffrage League the same year. Local suffrage groups began to organize in such key urban centers as Houston, Dallas, Galveston, and San Antonio. The strength and dedication of these emerging local chapters allowed for the formation of a stronger state organization. When TESA held its convention in San Antonio in 1913, seven local chapters sent delegates. The group elected Mary Eleanor Brackenridge, the organizer and leader of the San Antonio society, as president. By 1915 TESA had twenty-one chapters, and by 1918, eighty.
Historians have suggested that the increase of membership in suffrage associations after 1900 reflected not so much widespread advocacy of equality as a desire to protect the status quo. Though many suffragists believed that barring women from voting was unjust and discriminatory, others believed that the vote was the most useful tool for cleaning up their communities, whose corrupt and inefficient governments failed to protect the health and safety of their families. Thus, women within TESA may have had different reasons for identifying themselves as suffragists, not to mention different approaches to achieving the goal.
From the beginning, men were included in TESA, although Blacks were essentially excluded. The NAWSA constitution specified that groups could not gain membership in the national organization directly. Instead, they were forced to apply through individual state entities such as TESA. When the El Paso Colored Woman's Club applied in 1918, the TESA leadership refused to act upon its request, thus denying the group access not only to state but to national membership. The dominant belief among the leadership was that inclusion of Black suffragists would alienate not only White male voters outside the organization but also some members within TESA.
After Mary Brackenridge's term, Annette Finnigan was again chosen to lead TESA in 1914. The three primary objectives of TESA were to support the national agenda as defined by NAWSA, to lobby for a state suffrage amendment, and to assist local groups in promoting the cause. The year 1915 was a watershed year for the suffragists. Finnigan canvassed each legislator before the start of the biennial session regarding his position on woman suffrage and, with her colleagues, lobbied effectively enough that the enfranchisement bill fell only two votes short of passage. Minnie Fisher Cunningham, of New Waverly and Galveston, was elected president of TESA in 1915 and served in this position until victory in 1919. By the end of 1916 opposition to woman suffrage had solidified behind Governor James Ferguson and anti-prohibitionist leaders. It included a group organized by Pauline J. K. Wells, the Texas Association Opposed to Woman Suffrage. Although TESA had strengthened its organization and stepped up activities, it did not achieve passage of either the presidential suffrage bill or the primary suffrage bill, both of which were introduced in the 1917 legislature. Later in the year the group's energies turned toward the impeachment of Governor Ferguson through the Woman's Committee of Good Government and, following the national organization's lead, TESA organized its members for the war effort. It set up an Emergency Committee and a Food Conservation group, sold war bonds, and fought vice. With a special legislative session called for February 1918, TESA lobbyists promoted a women's primary suffrage bill that became law on March 26 with the signature of the new governor, William P. Hobby. During the seventeen days available, 386,000 Texas women registered to vote. TESA organized citizenship schools to instruct the new voters on how to fill out and turn in a ballot as well as other topics.
When the federal woman-suffrage amendment failed to clear Congress in 1918, TESA began an intensive campaign to amend the state constitution. The bill sailed through the legislature, which chose a date in May 1919 for the referendum required for a constitutional amendment. Despite the labors of TESA's ratification committee and a thorough and energetic publicity drive, the measure failed by some 25,000 votes. Minnie Cunningham attributed the defeat in part to the inclusion of a provision that disfranchised the many resident aliens in Texas, who naturally voted against the amendment. TESA members lobbied in the Capitol corridors and watched from the gallery when the Texas legislature met later in the summer to consider the long-delayed federal constitutional amendment. Its passage by both houses made Texas the first Southern state and the ninth in the nation to ratify the Nineteenth Amendment. TESA members gathered for their victory convention in October 1919. Their mission achieved, they voted to dissolve and convert the organization into the League of Women Voters of Texas.