MADISON, WI (WTAQ) - Democrat Tammy Baldwin leads the money race for Wisconsin’s open U.S. Senate seat.

The Madison congresswoman said she raised almost $4.6 million from July through September, while her Republican opponent Tommy Thompson raised $3.6 million.

Thompson, a former governor, said his war chest went dry soon after he won a hard-fought four-way GOP primary in August. But since then, he has raised $2.2 million – but Baldwin raised more, with almost $3.6 million.

The Thompson campaign said almost two-thirds of his donors gave $100 or less.

Baldwin said she had about $3.5 million on hand as of October 1st, while Thompson had around $2 million.

The so-called “money race” among the candidates is not as important as it used to be, because outside groups are now outspending the hopefuls several times over. A recent federal report said outside groups have spent $21 million on the Wisconsin Senate race – the second-highest among Senate contests in the country.

New Jersey Governor Chris Christie will campaign for Thompson on Wednesday in Green Bay.