The bitter and costly Texas governor's race entered its final stretch with an increasingly confident Republican Gov. Bill Clements predicting a comfortable victory and Democrats hoping that a $1 million get-out-the-vote drive will help Attorney General Mark White spring an upset.

On his last day of campaigning today, Clements will be joined by Vice President Bush in Houston and Dallas and plans to wind up with a rally at the Alamo in San Antonio.

White, scrambling to encourage a strong Democratic vote, spent yesterday working black churches in Houston and will devote his time today to Hispanic voters in the Rio Grande Valley before ending up at his birthplace in traditionally Democratic east Texas.

In the final days of the campaign, the perceptions of the two campaigns were strikingly different.

Clements predicted he will get at least 52 percent of the vote tomorrow. Veteran Republican political consultant Stuart Spencer, who is working for Clements, said, "I don't expect a big win, I expect a nice win."

But White's campaign manager, David Doak, said yesterday the race was "tight as a tick," and said a strong Democratic turnout would swing the race to the challenger.

Those predictions were based on poll data that each campaign has been following in the past week.

Clements' polls, according to his campaign manager, Jim Francis, have shown the governor gaining strength every day but one last week, with White slipping. The tracking is being done by GOP pollster V. Lance Tarrance of Houston.

"We've improved our position all week long," Francis said yesterday. "I am very comfortable about where we are."

The Clements campaign refused to release its figures, but campaign sources said Clements was leading White by approximately 20 points, with a considerable percentage undecided. The Clements campaign believes that many of those still undecided will not vote.

In contrast, White's polls showed him with a 5-point lead as of last Tuesday night. Doak said that as of Saturday, the tracking estimated White's lead at only "a point or two up." He attributed the decline to technical changes in the poll sample rather than a reduction in White's strength.

"If we have a good turnout . . . if that system works, we win," Doak said.

The system he referred to is a coordinated voter identification program funded jointly by White, Democratic Sen. Lloyd M. Bentsen, the overwhelming favorite to defeat GOP Rep. Jim Collins tomorrow, and other statewide candidates.

Organized by Louisiana political consultant Dan McClung, the operation is geared to get 1.5 million Democratic voters to the polls.

Many Democratic strategists say they are surprised that White is still competitive and that with the race close, McClung's operation could be the challenger's key to success. But the unanswerable question is whether those "Democratic" voters will also vote for White, a conservative trying to run as a populist.

White needs strong support among Texas' black and Hispanic voters, but the Clements campaign has worked hard to deny him those votes, especially among Mexican Americans. Clements has flooded the Hispanic areas of the state with direct mail, television and radio ads reminding voters that in 1975, White opposed extension of the federal Voting Rights Act to Texas.

The most effective ad shows former presidents Kennedy and Johnson along with President Reagan who signed the Voting Rights Act extension last summer.

The Clements' camp believes the incumbent might capture 40 percent of the Hispanic vote and White's pollster, Dick Morris, said last week that his polls put Clements' Hispanic vote at about 30 percent.

In his final television blitz, White is concentrating on three things. One is the fact that Clements has spent nearly $12 million, to White's $5.2 million, to win reelection. Another ad, showing a banquet table and caviar, says that while the economy may look good to the rich, things are tough on Main Street, a reference to the state's 8.4 percent unemployment rate.

The third issue is utility rates, which White feels symbolizes voters' anger with Clements. But Francis said that while the utility issue originally hurt the governor, it no longer poses a danger to his reelection.

Clements' final ads are designed to attract support of women voters, who make up a majority of the undecided vote, to blunt White on the utilities issue and to draw a comparison between the governor, who is portrayed as a "businessman and manager," and White, who is called a "lawyer-politician."