(CNN) Senate Democrats are eager to make Donald Trump pay a political price for nominating staunch conservatives to fill out his Cabinet, hoping to exact revenge for the GOP's stubborn opposition to President Barack Obama's nominees.

But there is little they can do about it -- and some top Democrats are now coming to regret it.

That's because Senate Democrats muscled through an unprecedented rules change in 2013 to weaken the power of the minority party to filibuster Cabinet-level appointees and most judicial nominees, now setting the threshold at 51 votes -- rather than 60 -- to overcome tactics aimed at derailing nominations.

With the Senate GOP poised to hold 52 seats next Congress, some Democrats now say they should have thought twice before making the rules change -- known on Capitol Hill as the "nuclear option."

"I do regret that," said Sen. Chris Coons of Delaware, a Democrat who voted for the rules change three years ago. "I frankly think many of us will regret that in this Congress because it would have been a terrific speed bump, potential emergency break, to have in our system to slow down nominees."

With their power weakened, Democrats are weighing how to make life difficult for the Senate GOP.

They are planning on making the fight over Rep. Tom Price's nomination to lead the Health and Human Services Department a proxy war over the GOP's plans to to dramatically overhaul Medicare. They want to turn Steven Mnuchin's nomination to lead the Treasury into a battle over regulating Wall Street. And they want to make Sen. Jeff Sessions answer for his hard-line stands on civil rights issues and against comprehensive immigration reform.

Senate Democrats plan to make speeches and mount objections to Senate Majority Leader Mitch McConnell's efforts to quickly schedule votes to confirm much of Trump's Cabinet by the time he is inaugurated in January. Under the rules, they could delay votes from taking place for a few days at a time, temporarily slowing down the Trump agenda.

But they ultimately won't be able to stop those nominees -- unless Republicans defect and join the Democratic opposition. And that fact has begun to grate at Democrats, who have complained bitterly at Republicans' stands against Obama's nominees -- most notably their unprecedented refusal to even give the President's Supreme Court choice, Merrick Garland, a hearing.

Some Democrats realize they've made life harder for themselves.

"In specific circumstances, we may regret that we can't block a nomination," said Sen. Richard Blumenthal, D-Connecticut. "But I think that the American people want action, and they want the process to work. And they want the folks whom they have elected to actually do the job and get stuff done."

One person who seems to be having buyer's remorse over the change in filibuster rules: Sen. Chuck Schumer, the incoming Democratic leader. Schumer told The Washington Post last month that he privately lobbied Senate Democrats in 2013 to maintain the 60-vote threshold for Cabinet-level nominees, but: "I didn't prevail."

Asked twice at a news conference last week, Schumer declined to say if he thought invoking the nuclear option was a mistake. He instead sharply criticized Price's views on Medicare, and said, "That's all I'm going to say."

Schumer weighed in Monday on one example where Democrats' hands are apparently tied on a nominee they disapprove of: retired neurosurgeon Ben Carson, who was picked by Trump to head the Department of Housing and Urban Development.

"I have serious concerns about Dr. Carson's lack of expertise and experience in dealing with housing issues," Schumer said in a statement. "Someone who is as anti-government as him is a strange fit for Housing Secretary, to say the least."

The man who pushed through the rules change -- retiring Senate Minority Leader Harry Reid -- said he has no qualms for making that change, pointing to how the GOP was holding up Obama nominees at all levels, notably the DC Appeals Court.

"Yes, we changed the rules," Reid said last week. "We had to change rules because we now have a DC Circuit that functions, we've got 98 judges, and we have a functioning National Labor Relations Board .... And remember, with now 48 senators, we only need to pick up a few Republicans of goodwill to stop some of these nominations."

Oregon Sen. Jeff Merkley, a champion in the push to reform the filibuster, said, "I have absolutely no regret" in invoking the nuclear option.

One area where Senate Democrats do hold power over Trump is his nomination of Gen. James Mattis to lead the Defense Department. That's because Congress needs to approve a waiver allowing him to serve in that capacity since his 2013 retirement from the Marines is within a seven-year waiting period required for active duty personnel from taking the top civilian post. Senate Democrats can mount a filibuster, requiring 60 votes in the Senate for approval.

Schumer has not yet taken a position on the waiver. And a senior Senate Democratic aide said that many in the caucus would not be comfortable granting a waiver before fully assessing Mattis' views.

In the House, Democratic leader Nancy Pelosi came out Tuesday against fast-tracking the waiver, as did Rep. Adam Schiff, a member of the House Intelligence Committee.

But if the waiver is approved, Mattis -- like other Cabinet-level nominees -- would only need GOP support to get confirmed lead the Pentagon.

When he pushed through the changes in 2013, Reid said the GOP would benefit as well.

"The changes that we made today will apply equally to both parties," Reid said at the time. "When Republicans are in power, these changes will apply to them as well. That's simple fairness. And it's something both sides should be willing to live with to make Washington work again, that is also simple fairness."