Sen. Elizabeth Warren (D-Mass.) railed against Senate Minority Leader Mitch McConnell (R-Ky.) on Wednesday for failing to support her student loan refinancing proposal, which the Senate killed in a 56-38 vote that failed to overcome a filibuster earlier in the day.

Warren's bill would have enabled millions of Americans to refinance their student loans into cheaper debt by increasing taxes on wealthy households. Following the bill's defeat, Warren told MSNBC that McConnell, who called the proposal a "show vote," has made clear where his allegiance lies.

"Mitch McConnell is there for millionaires and billionaires," Warren said. "He is not there for people who are working hard playing by the rules and trying to build a future for themselves."

When MSNBC's Chris Hayes asked Warren how she planned to fight back, the senator gave a response that could shake things up in Kentucky, where McConnell faces a tough race for reelection against Democrat Alison Lundergan Grimes.

"One way I'm going to start fighting back is I'm going to go down to Kentucky and I'm going to campaign for Alison Lundergan Grimes," Warren said. "She's tough, she's feisty, she endorsed the student loan bill, said she wanted to bring down interest rates for Kentuckians. ... So my view is I'm going to get out there and try to make this happen for her."

Following the Senate vote, Grimes released a statement slamming McConnell for his "blatant disregard" for Kentuckians burdened by student loan debt.

Warren said Grimes is just what Washington needs.

"You get Alison Lundergan Grimes in there and I feel like she could almost single-handedly get rid of some of the gridlock here in Washington," Warren said.

Though this is the first time Warren has indicated her intent to back Grimes on the campaign trail, McConnell has already assailed Grimes by linking her to the senator from Massachusetts.

In a September fundraising email, McConnell told supporters that Grimes had hired "the top fundraiser from Elizabeth Warren's record-setting campaign," calling Warren "the most liberal, anti-business member of the Senate." He warned that Grimes could have similar success.

In May, McConnell lamented Grimes' front-and-center appearance on the website for the Democratic Senatorial Campaign Committee in another email to supporters, saying the committee holds events "with the likes" of Warren.