Mr Morales, a 46-year-old Hispanic American with 17 years in the classroom and zero political experience, has driven more than 50,000 miles round Texas, campaigning in petrol stations and returning calls from payphones. He has been dubbed Don Quixote in a pick-up truck, and the odds are against him.
But by pitching himself as the average Joe, he first won the Texas Democratic nomination for US senator in defiance of the party establishment, and has come within at least striking distance of Senator Gramm.
He enjoys almost folk hero status among the state's large Hispanic population. He has enthused Texas teachers with his promise to make public education his first priority if he wins. And he is fast winning converts among them to the idea of sending a high school civics teacher to Washington.
A Texan-born father of two, Mr Morales was recently named "most spirited teacher" three years in a row at Poteet High School in Mesquite, south Texas. Soon after winning a local city council seat, he asked his government class whether he should run against Senator Gramm - and when they said yes, he did.
He took a five-month leave of absence from his job, and says he cannot lose in the election - because if he doesn't win, he'll go straight back into teaching."If you cannot get elected without playing games, then we're all hypocrites and we're all cynical and we don't want any change," he said. "Why not me? Why not an ordinary man?" Long-running differences over education policy have hardened in this year's election. Candidate Bob Dole has attacked the political power of the teachers unions while Bill Clinton has proclaimed himself a friend to "the people who give their lives to education".
Teachers in public schools have gravitated to the Democrats. Mr Morales was given a speaking slot at the Democratic convention, where a tenth of delegates were teachers. "There are two reasons I'm able to stand in front of you: money, and education," he said.
He also met an enthusiastic welcome when he arrived at the Texas Federation of Teachers' summer conference in his truck.
Mr Morales is a long-standing TFT member, and he promised to fight cuts in college loans and education spending. Senator Gramm, by contrast, has won the TFT's hostility for backing school voucher programs and cuts in federal spending on education.
Mr Morales trails Senator Gramm by 12 per cent in the polls, a wide but not impossible margin. Sam Attlesey, a political writer for the Dallas Morning News, said he thought Mr Morales was genuinely without political ambition, and has appealed to public disenchantment with established politicians.
His weakness is his failure to outline a policy agenda that appeals to voters beyond his everyman image, said Mr Attlesey. His views do not seem to rest easily with the mostly white, conservative Texan electorate, to whom he has spoken out in favour of gun control, abortion rights, and affirmative action for ethnic minorities, for example, But his biggest problem of all is money. Senator Gramm is a senior Republican whose fund-raising abilities are legendary.
After spending $25 million (Pounds 16m) to win just a tiny fraction of the Republican primary vote, in a presidential campaign that was a disastrous failure, Senator Gramm looked vulnerable. But he still has more than $3m in campaign funds to defend his senate seat.
Mr Morales by contrast has so far raised only $150,000 in small contributions, though he proved his appeal by beating two local Democrat congressmen in the primary race.