Democrats who have been waiting like an eager suitor for the New Hampshire governor, Maggie Hassan, to just say “yes” got their wish on Monday when Ms. Hassan finally announced that she would run for the United States Senate.

“The Granite State needs a senator who knows that New Hampshire comes first,” she said in a video announcement.

Both parties had been waiting to see what Ms. Hassan, who drew a lot of attention when she vetoed a budget passed by the State Legislature this year, would do. She is widely viewed as the biggest potential problem for Senator Kelly Ayotte, the freshman Republican incumbent.

Within minutes of Ms. Hassan’s announcement, the National Republican Senatorial Committee pounced. “Under Hassan’s failed leadership as a do-nothing governor, New Hampshire’s economy has stalled and businesses have threatened to leave the state because of her open hostility to pro-growth policies that would create good-paying jobs for Granite Staters,” the organization said in a news release.

But Ms. Hassan has been a largely popular governor who has proved she can win statewide, and will be running in a state that tends to lean toward Democrats in presidential years. President Obama won the state twice, and John Kerry narrowly won it in 2004.

Mindful of this dynamic, Ms. Ayotte has been skillfully moving a bit to the left in the Senate in recent months.

An average of polls calculated by Real Clear Politics found that Ms. Ayotte leads Ms. Hassan by 4.5 percentage points in a hypothetical matchup. But that has tightened since the middle of the summer.

Ms. Ayotte, 47, looks as if she will be well financed going into the contest. According to a report from WMUR.com, she already has $5 million in cash on hand for her re-election effort and has raised $1.6 million in the third quarter of the year.

Ms. Hassan, 57, has signaled that she will cast herself as a Washington outsider who is fiscally responsible and able to work across party lines.

Expect this race to be among the most closely watched among a dozen hot contests.

Alan Rappeport contributed reporting.