ST. LOUIS — It may not be top on the minds of many voters, but Republican Senate candidate Josh Hawley says Sen. Claire McCaskill’s opposition to having the 2020 census ask people about their citizenship status is exactly the reason voters should oust her.

For Mr. Hawley, it’s a common-sense question and the answer could enhance Missouri’s political muscle in Washington.

He said Ms. McCaskill’s antipathy to the census question shows that she sides with Democratic Party leaders over the interests of her state.

That is the crux of Mr. Hawley’s message strategy in the final stretch of an incredibly close race that could determine party control of the Senate, he said in an interview with The Washington Times.

“Sen. McCaskill would love to give more representation to California. That’s what will happen,” Mr. Hawley, the state attorney general, said of the decennial count that determines the number of representative each state sends to Congress.

“Places like California and New York that have greater numbers of illegal immigrants, they are going to end up with more representation, and we’ll lose seats. She is fine with that, though,” he said. “That just strikes people in Missouri as craziness. They just don’t understand it. I don’t understand it.”

The issue fits neatly into Mr. Hawley’s plan to harness the furor surrounding Supreme Court Justice Brett M. Kavanaugh’s confirmation. He said Ms. McCaskill’s “no” vote shows she is beholden to Washington Democrats’ “extreme agenda.”

“Block conservative judges, throw open our borders, raise taxes on the middle class. That is their agenda,” he said. “They are hungry for power, and they will do just about anything to get it.”

The Democratic agenda he cited echoes the rally cries of President Trump, who carried Missouri by nearly 19 points in 2016 and is a key ally and guiding light for the Hawley campaign.

The McCaskill campaign refused to answer questions about the senator’s stance on the census citizenship question or the effects of Justice Kavanaugh’s confirmation.

Ms. McCaskill has called the Trump administration’s attempt to put the citizenship question on the census “blatantly political.” As the ranking member of the Senate Homeland Security and Governmental Affairs Committee, which oversees the Census Bureau, she joined other Democrats in demanding a hearing on the issue.

The census question is now before the Supreme Court. The Trump administration’s case was dealt a blow Thursday when it confirmed that then-Trump political adviser Steve Bannon was instrumental in pushing the Census Bureau to ask about citizenship in the 2020 count.

The momentum Mr. Hawley sees for his campaign is not reflected in the polls, which have shown the race in a virtual tie for months.

Mr. Hawley had a narrow 1-point lead, 45 percent to 44 percent, in a Reuters/Ipsos/UVA Center for Politics poll released last week, but the poll’s 3-point margin of error means it is a statistical tie.

On the campaign trail, Mr. Hawley is hammering Ms. McCaskill for doing the bidding of Democratic leaders, including voting against both of Mr. Trump’s Supreme Court picks while voting for both of Mr. Obama’s.

He travels the state in a bus decorated with a huge picture of Ms. McCaskill, Senate Minority Leader Charles E. Schumer and House Minority Leader Nancy Pelosi next to text that reads: “Stop Schumer, fire Claire. Don’t let the liberals take over.”

The controversy over Justice Kavanaugh, including unsubstantiated sexual-misconduct allegations from his high school and college days and the resulting raucous left-wing protests occurred just as voters were starting to pay attention to the elections. The timing was auspicious for the Hawley campaign, which is locked in a neck-and-neck race against the two-term incumbent.

He said the spectacle of the confirmation process galvanized support for him among Republicans and independents who were outraged by the Democrats’ conduct, and it boosted “all phases” of the campaign.

In just the three weeks of the confirmation showdown, from late September to early October, the Hawley campaign received more small-dollar contributions than it had expected to receive for the entire fall campaign, he said.

“It is just such a revelation. The Kavanaugh debacle [showed] what the Democrats are about,” said Mr. Hawley.

He said it sharpened the focus on the choice facing Missouri voters.

“It is a big bright choice between what you see in the Kavanaugh debacle that these Democrats want to do. It is the extreme agenda that they have: Block conservative judges, throw open our borders, raise taxes on the middle class,” Mr. Hawley said. “That versus the agenda that this state voted for in 2016, which is to rebuild this country. It is a stark choice and that choice is on the ballot.”

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