WASHINGTON — Their grip on the Senate majority slipping, anxious Democrats aggressively courted female voters Saturday on the final weekend of a midterm campaign that will decide the balance of power in Congress and statehouses during President Obama’s final years in office.

At the same time, some Republicans offered a softer tone as party leaders began to outline plans for a Republican-controlled Congress even with polls suggesting more than a half dozen Senate contests are deadlocked.

“We want to engage members from both parties in the legislative process, to get our democracy working again the way it was designed, said Senate Republican leader Mitch McConnell, who would ascend to majority leader if his party gains six seats.

Without getting specific, he predicted that Republicans would “be able to work with the president to ensure solid, pro-middle class ideas are signed into law.”

Plagued by poor poll numbers, Obama has avoided the most competitive elections, but used his last radio and Internet address before Tuesday’s election to seek support from women, who are expected to play a pivotal role in races from New Hampshire to Iowa.

“When women succeed, America succeeds,” the president said. “And we should be choosing policies that benefit women – because that benefits all of us.”

The election will decide control of the Senate, the House and 36 governors’ seats.

The Senate contests could dramatically shape the final two years of Obama’s presidency. Republicans already control the House and must gain at least six seats for a Senate majority in the Congress that convenes in January.

Republicans appear certain of at least three new seats – in West Virginia, Montana and South Dakota.

There are nine other competitive races, including six for seats currently in Democratic hands.

The head of the Democratic National Committee, Rep. Debbie Wasserman Schultz of Florida, said she was optimistic despite polls showing her party struggling just to maintain the status quo.

“Democrats will hold the Senate,” she said Saturday.

Her Republican counterpart, Reince Priebus, was campaigning with Gov. Scott Walker, R-Wis., and pointed to increasing signs that Republicans will have a good election night.

“I’m feeling pretty confident about where we are across the country,” he said.

Women were the focus in Kentucky on Saturday as Hillary Rodham Clinton, appearing with Alison Lundergan Grimes, endorsed a higher minimum wage and equal pay for women in remarks to more than 1,000 people at Northern Kentucky University.

“It’s not, as Alison rightly said, only a woman’s issue,” said Clinton, a possible 2016 presidential candidate. “It’s a family issue. It’s a fairness issue.”

Women’s votes have shifted sharply between presidential years and midterm elections. In 2012, women broke for Obama by an 11-point margin, according to exit polls. In 2010, when few candidates raised social issues as a major campaign theme, female voters split evenly between Democratic and Republican House candidates.

Democrats have put women’s health and reproductive rights at the center of Senate campaigns in Alaska, Iowa, North Carolina and especially Colorado.