Wisconsin took center stage today with the announcement that Rep. Paul Ryan will be the GOP’s candidate for vice president. But by Tuesday, the Badger State could be defined as much by a too-close-to-call Senate primary as by its newly elevated native son.

Tuesday is primary day in the state, and the race to win the Republican nomination for its open Senate seat has been described by operatives on the ground and inside the Beltway as “a coin flip.” Polling shows a near-tie between former Gov. Tommy Thompson and tea-party-backed businessman Eric Hovde, with Ryan’s predecessor in the House, Mark Neumann, running several points behind.

In the midst of that turbulent environment, presumptive GOP presidential nominee Mitt Romney and his new running mate will visit Waukesha, where they will be joined by Republican National Committee Chairman Reince Priebus.

Whether Ryan’s move to the national ticket will have an immediate effect on local voters is unclear. Ad time is locked up, and all the candidates have dug in on their messages. But the same qualities that make Ryan so polarizing nationally – that he galvanizes conservatives for him and Democrats against him – could have local effects down the line as Wisconsin Republican hopefuls rushed today to grab his coattails.

“Absolutely,” Thompson said in a press call, when asked whether the Ryan announcement helps with his campaign. “There’s no question about it. I think most people know that Paul and I are close friends and that we teamed up on many issues, especially on Medicare.

“The worst thing that could happen [would be to have a] Senate still controlled by [Majority Leader] Harry Reid with Mitt Romney and Paul Ryan” in the White House trying to enact entitlement reform into law, Thomspson continued, noting he had made suggestions to Ryan’s controversial budget plan that would transition Medicare into a voucher-like system by 2020.

Thompson, who has been slipping in the polls, made the most aggressive effort to tie himself to Ryan, though Neumann also released a statement.

The flipside, however, is that by November, Democrats will have spent months trying to define Ryan as an “extreme” conservative whose entitlement reforms and cuts to the budget are outside mainstream thinking. And those sound bites of candidates tying themselves to Ryan might end up hurting more than helping. In many ways, the Republican candidates in Wisconsin touting Ryan are taking the same risk Romney is.

Thirty-six percent of registered Wisconsin voters have a favorable opinion of Ryan, while 29 percent hold an unfavorable view and 30 percent say they don’t know enough about him, according to a July poll from the Marquette University Law School. The unfamiliar 30 percent are likely to be pivotal.

And both parties believe they’re in the better position to win.

“This further highlights the clear choice before Wisconsin voters in November between a Republican candidate who wants to save Medicare, focus on job growth and rein in out-of-control Washington spending versus … Tammy Baldwin, who voted to cut Medicare to pay for more government while maxing out the government credit card to the tune of trillions of dollars,” National Republican Senatorial Committee Communications Director Brian Walsh said.

A Republican strategist working with the Hovde campaign suggested the Ryan pick ensures maximum enthusiasm for the party in the general election while focusing on fiscal responsibility, which was also focus of Democratic Sen. Russ Feingold, who was unseated by tea-party-backed Ron Johnson in 2010 after three terms.

Democrats, on the other hand, believe their jobs are easier now that Ryan will be out front and talking about his plan. Republicans who had once shied away from his budget in the face of backlash at the polls and from social groups such as Catholic nuns will now have to talk about the blueprint again, at a minimum, or embrace it.

“Now you don’t have to spend time or capital explaining the Ryan plan because everyone’s going to know what it is,” said one Democratic operative working in the state, adding, “If you’re going to be moved by Paul Ryan being on the ticket, you already are … you’re a high-information Republican voter.”

In a telephone interview today, Rep. Chris Van Hollen, Ryan’s partner on the Budget Committee and former head of the House Democrats’ campaign arm, said Ryan’s selection for the national ticket will only help Democrats downballot across the country.

“I think it sharpens the contrast in a way that helps the president [and] in a way that helps Democrats [because] while this will excite the base of the Republican Party, it leaves independent voters in the cold,” the Maryland lawmaker said. “The Republican budget is an uncompromising blueprint for tax breaks for folks at the very top at the expense of everybody else.”

Ryan is just the latest on an elite list of Wisconsin Republicans to rise to the top of the GOP crop, from Preibus to polarizing-but-idolized-by-the-right Gov. Scott Walker.

The prominence of the Wisconsin Republican has raised the stakes statewide to build momentum for the party, whether it’s by delivering a state that hasn’t gone red for president since 1984, helping the GOP take back the Senate or even protecting Ryan’s House seat, which could be vulnerable as he focuses on his national run.

Though Ryan won re-election last cycle by a 2-to-1 margin in his Southwestern district, he faces a self-made and organized Democratic opponent in former Kenosha County Supervisor Rob Zerban, who has worked relentlessly to convince the establishment that his is a real race.

Abby Livingston contributed to this report.