Gov. Bill Clements, the $10 million man of Texas politics, rolled his reelection campaign into San Antonio and quickly showed why many political experts in the state believe he will be hard to beat on Nov. 2.

On the Sept. 16 holiday commemorating the beginning of the fight for Mexico's independence, Clements continued his careful courtship of Mexican Americans by dedicating an addition to a monument honoring Hispanics in Texas, flashed his clout with Washington by announcing that the city had been granted status as a foreign trade zone and surprised everyone by saying that his new poll shows him leading in the heavily Hispanic area of south Texas.

The four-hour campaign stop was a powerful reminder of the assets Clements brings to his contest with Democratic Attorney General Mark White, a race that is considered one of the most important gubernatorial elections in the country because of the state's pivotal role in national elections.

Clements is throwing everything possible at his underfunded opponent, and in the past month has opened up a small lead on White, whose campaign is lagging because of disorganization and lack of enthusiasm among many Democrats.

A private poll taken in late August gave Clements a 37-to-34 percent lead. Clements' latest poll, completed last weekend, reportedly gives him a lead of 12 percentage points, a sharp increase over a survey taken last summer.

White's latest poll puts the race even and campaign aides acknowledge that White has lost ground in recent weeks.

But the polls also show that perhaps 25 percent of the voters are still undecided, which confirms the belief that the outcome of the race will go right down to the closing of the polls on Election Day.

Clements knows that anything less than an all-out effort could make him a historical footnote as the first Republican governor in Texas in 105 years, rather than the man who ushered in two-party politics in the Lone Star State.

Four years ago, backed by $7 million and an organization that surprised divided Democrats, Clements, a former oilfield worker who founded SEDCO, the largest drilling company in the world, sneaked into the governor's mansion by a margin of fewer than 17,000 votes out of more than 2.35 million cast.

Today, it isn't possible for Clements to sneak up on anybody. Brash, brusque, ornery, blunt and bull-headed, Clements has polarized Texas voters as few politicians ever have and the Democrats have put aside their normal fratricide in a united effort to unseat him.

On paper it shouldn't take much to do that, for Clements starts the final six weeks of the campaign with a number of obvious liabilities. The first is personality. "Mark White is way ahead in this race in one area," said a Clements supporter, "and that's style."

Clements' habit of popping off has left him a laundry list of embarrassing quotes, such as the time he referred to the Mexican oil spill of a few years ago as a "tempest in a teapot," and his recent comment that he didn't "know of any housewife who is qualified" to be on the state board that regulates public utilities.

That style has given Clements some of the highest negative ratings of any politician running this fall. Republicans admit that almost one-third of the electorate in Texas doesn't like Clements, and Democrats say the number approaches 40 percent, which could be politically fatal.

Clements' second problem is the Texas economy. "The economy of Texas is not as healthy today as when Bill Clements took office," White said this week.

The unemployment rate in Texas rose from 5.3 percent in August, 1981, to a peak of 7.0 percent last July, then fell last month to 6.7 percent. More than 500,000 Texas are out of work.

Clements acknowledged today that things have become worse. "There probably has been a slight decline from our good health of a year ago," he said in answer to a question.

But the governor's basic message as he troops the state is that Texas is still better off than the rest of the country.

"No state is recession-proof," he said, but the economy of Texas "is the most recession-resistant in the nation."

As evidence, Clements cites the fact that a record 6.8 million Texans are at work, while the number of new jobs has risen an average of 220,000 in each of his years in office. Texas, he said, has the lowest unemployment rate of the 10 largest states and continues to have one of the most attractive business climates in the nation.

Democrats say their polls show the economy is the No. 1 issue with voters, but Clements' poll-taker, V. Lance Tarrance of Houston, argues that it does not yet threaten the governor because voters either believe the state economy is relatively healthy or don't blame Clements for what is perceived as a problem created in Washington.

Still, Clements has been running almost like an underdog, and the Reagan White House has been generous with its help.

When farmers in west Texas asked for disaster payments, Clements persuaded the White House to let him make the announcement, rather than the Democratic congressmen in that area. When border businesses needed economic aid last month, Clements got the Reagan administration to let him announce a $200 million loan fund from the Small Business Administration.

Clements, in a round of radio advertising that caught the White campaign off guard, also opened a harsh attack on White's record as attorney general. Clements has criticized White for losing big cases and running a sloppy operation.

Clements' camp also has attacked White for his 1975 opposition to extending the Voting Rights Act to Texas, a position that has cost White crucial support in the Mexican-American community.

Clements captured roughly 25 percent of the Mexican-American vote in 1978 and his staff workers now believe he can do significantly better than that this fall.

Any Democratic candidate would have a chance of beating Clements because of the fact that Texas is still a Democratic state in voter registration. And in White, 42, who comes from the party's conservative wing, the Democrats have what should be an ideal person to hold the disparate wings of the party together.

But the White campaign is in deep trouble financially. Clements has raised close to $9 million to date. David Doak, White's campaign director, said his candidate can win even if Clements outspends them by 3 to 1. But reports from around the state suggest that White may not raise even that much.

Democratic officials also said White's campaign has generated little enthusiasm even from traditional Democratic voters. By contrast, Clements' organization around the state is visible and active, and he will tap more than 30,000 volunteers to run phone banks to draw out his supporters.