Republicans entered the 48-hour sprint to Election Day confident they can expand their Senate majority while bracing for a knife fight over the House, hoping their “can’t go back” message on the border and the booming economy eclipses the wave of college-educated women and suburbanites looking to punish President Trump.

Mr. Trump wrapped up the midterm campaign by rallying Sunday with Tennesseans who could determine whether the GOP expands its 51-49 Senate majority, as Republican Rep. Marsha Blackburn vies with former Democratic Gov. Phil Bredesen for an open Senate seat, before heading to Missouri Monday to try to flip a Democratic seat into the red column.

The events will cap a whirlwind tour for the president, who is focusing on the threat of illegal immigration and bitter fight over Supreme Court Justice Brett M. Kavanaugh’s confirmation to rally red state voters against vulnerable Senate Democrats in 10 states that Mr. Trump won two years ago, even though his economic message is better suited toward winning centrist, suburban voters who will determine House control.

“I think what you’re seeing with the president is he’s made a strategic decision that his ability to claim victory on election night will be by adding seats in the United States Senate,” said former New Jersey Gov. Chris Christie, a Trump ally, on ABC’s “This Week.” “And he doesn’t want to take the risk of looking like he’s trying too hard in the House, because then he may get blamed for losing there.”

Mr. Trump told reporters at the White House before heading off to campaign Sunday, “We’re going to do well in the House, but as you know, my primary focus has been on the Senate, and I think we’re doing really well in the Senate.”

Democrats increasingly confident of a House takeover acknowledged their long odds in the Senate, yet refused to wave the white flag.

Sen. Chris Van Hollen of Maryland said his party faces the “toughest political map any one party has faced in 60 years,” though he refused to concede defeat.

“We do have a path. It is a very narrow path,” Mr. Van Hollen, chairman of the Democratic Senatorial Campaign Committee, told “Fox News Sunday.”

Likewise, the Republican National Committee said the GOP can preserve its House majority, arguing voters won’t cede 23 seats or more seats to Democrats while the economy roars to life. Republicans were bolstered by government figures released Friday showing strong job creation and broad-based wage gains.

“Americans are making more money. More jobs are coming back. That is a great closing argument in a lot of these Houses races that are within the margin of error,” RNC Chairwoman Ronna McDaniel told ABC. “And [voters are] going to say Republicans have offered a record of results and Democrats are offering resistance and going back.”

Two-thirds of voters say they’re satisfied with the economy, and 74 percent said they’re satisfied with their own financial situation, according to an NBC-Wall Street Journal poll released Sunday.

Yet, six in 10 voters say they want a change from the way Mr. Trump is leading the country, meaning the president’s polarizing style likely will play a big role in election night results.

“If the GOP fails to hold the House, the president will only have himself to blame,” Peter Hart, a Democratic pollster, told NBC.

Fifty percent of likely voters say they want Democrats to lead Congress overall, while 43 percent want Republicans to retain the gavels, the poll found.

Democrats also are hoping to score a number of gains at the state level, including targeted governorships in Georgia, Florida and the Midwest, while flipping control of a number of statehouses.

Revving up the base

Democrats lead among black voters, Hispanics, young people, women and independents, while Republicans hold an edge with older Americans, men and whites.

White women without college degrees prefer Republicans by a 12-point margin, though white women with degrees clearly prefer Democrats, 61 percent to 33 percent.

Both sides are revved up ahead of Election Day, with 85 percent of Democrats expressing a high level of interest in the elections compared to 82 percent of Republicans.

“This is going to be directly related to turnout. I think, in the next two days, the team, the side that gets the most turnout and handles the ground game appropriately and aggressively is going to be the one that wins,” said Rep. Tim Ryan, Ohio Democrat, on Fox News’ “Sunday Morning Futures” program. “And I feel good about our turnout across the country, and I think we’re going to take the House back.”

Mr. Trump’s aides say the president will be campaigning right to the end, planning a series of get-out-the-vote interviews with local media at the White House Tuesday before settling in to watch the returns.

Mr. Van Hollen, meanwhile, said Mr. Trump’s strident style is keeping his red state incumbents in the game, while giving Democratic challengers in places such as Texas, Tennessee, Arizona and Nevada a shot.

“What the president is doing is driving away the independent voters and swing voters, and a lot of moderate Republican voters in these swing states,” Mr. Van Hollen said.

Yet Senate Democrats such as Bill Nelson of Florida, Joe Donnelly of Indiana and Claire McCaskill of Missouri are locked in tight races against formidable opponents, while polls say Sen. Heidi Heitkamp is far behind Republican Rep. Kevin Cramer in North Dakota.

Mr. Van Hollen said people have counted out Ms. Heitkamp before, only to regret it. But the GOP is feeling good about its prospects.

“We’re not only going to hold the majority, I think we’re going to add to it,” Sen. Thom Tillis, North Carolina Republican, told “Fox News Sunday.” “The map looks very good to us in about five or six different states.”

The Democrats’ hopes of blunting the GOP’s march or even flipping seats run through places such as Tennessee, where Mr. Bredesen is nipping at Ms. Blackburn’s heels in the race to replace retiring Sen. Bob Corker, a Republican.

Pop star Taylor Swift urged voters to back Mr. Bredesen, though Mr. Trump responded in kind late Sunday, opening his rally in Chattanooga with country star Lee Greenwood, who performed his “God Bless the USA” — a staple at Trump rallies.

“These rallies are the best thing we’ve done,” Mr. Trump told reporters Sunday, predicting the GOP would do well in the House and “really well” in the Senate.

“The level of fervor, the level of fever is very strong on the Republican side,” he said. “I can’t speak to the blues, but I can speak to the reds.”