Frustrated because his agenda is moving at a snail's pace in Congress, President Trump has demanded that the Senate change its rules and lower the threshold for most major pieces of legislation to a simple majority vote in order to stop obstruction by Democrats.

Most legislative measures, like government spending bills, however, are subject to a 60-vote procedural hurdle, known as the filibuster, that's needed to end debate and advance bills to a final vote. This is made possible by Rule 22 of the Senate rules, and senators are not keen on making such a drastic change to it.

"The very outdated filibuster rule must go. Budget reconciliation is killing R's in Senate. Mitch M, go to 51 Votes NOW and WIN. IT'S TIME!" Mr. Trump tweeted after Senate Republicans failed to pass any form of an Obamacare repeal, adding that they look like "fools." The president issued a similar request in mid-July and in May. ("Mitch M" refers to Senate Majority Leader Mitch McConnell, R-Kentucky.)

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But for two major priorities -- health care and tax reform -- Senate Republicans have relied on, or plan to use, the budget reconciliation process that allows certain legislation to pass with 51 votes instead of 60. Even with the lower threshold, Republicans were unable to pass a health care bill last month. As McConnell has said before, the rules are not the GOP's problem, and he dismissed the president's call to change them.

"It's pretty obvious that our problem on health care was not the Democrats. We didn't have 50 Republicans," he told reporters. "There are not the votes in the Senate, as I've said repeatedly to the president and to all of you, to change the rules of the Senate. There are not enough. It would require 50 or 51 Republicans to agree to do that and the votes are simply not there."

The Senate, along with the House, have recessed for the rest of August, and Republicans are planning to take up tax reform when they return to Capitol Hill in September. Republicans will use reconciliation, McConnell said, to try to pass an overhaul of the tax code.

With McConnell's opinion on the issue unchanged, it's pretty unlikely that the upper chamber will comply with Mr. Trump's demand to get rid of the filibuster for legislation. Rich Arenberg, an adjunct professor at Brown University who co-authored "Defending the Filibuster: Soul of the Senate," told CBS News that the filibuster is in the Senate's DNA and getting rid of it would turn the upper chamber into a majoritarian body, which is not what it was designed to be.

"I think that would damage the Senate and its historic role and it would be a disaster to do that," he said. "I wasn't happy that they did it on the nominations, but to do it on legislative matters would be far worse. It's important in that it requires the majority to work with the minority and come to a compromise."

Senate Republicans already took a risk when they eliminated the filibuster, also known as invoking the nuclear option, earlier this year to confirm Neil Gorsuch as a Supreme Court justice. After they took the plunge, a bipartisan group of 61 senators in April called on Senate leaders in a letter to preserve "existing rules, practices and traditions" in the Senate and not get rid of the filibuster for legislation.

Republicans, however, are not giving up on their quest to reform procedures on the Senate floor that they say promote delay tactics by the other party.

On one hand, Sen. James Lankford, R-Oklahoma, a former member of the House where the pace of floor movement is much faster than the Senate's, argues that the filibuster should remain intact.

"The Senate should not go to a 51-vote majority for every vote. Because the Senate is the one entity in the federal government where the minority view is heard and deliberation is protected," he wrote in a recent op-ed published by The Wall Street Journal.

On the other hand, Lankford said something must change.

"First, the minority party has for months abused Senate rules to stall the nomination process and therefore the entire Senate calendar. Second, the arcane rules of the Senate always force a painfully slow legislative pace," he wrote.

The Senate should consider doing three things, Lankford said:

Reduce floor debate time for executive nominees from 30 hours to 8 hours or less



Lower the threshold on the "motion to proceed" that begins legislative debate and amendment consideration from 60 votes to 51



Consider dual tracking in which senators can debate and vote on multiple pieces of legislation



Several Senate Republicans told CBS News that they like the idea of at least lowering the threshold for the "motion to proceed" vote.

"One area that I really do like is the suggestion that we'd be able to get on a bill without having to have a 60-vote margin just to get on it because how do you actually get in to discuss it and work on it unless you can bring it to the floor and start publicly discussing what you want to do with it," said Sen. Mike Rounds, R-South Dakota.

"I am intrigued with Senator Lankford's idea about eliminating the filibuster on the motion to proceed," said Sen. Roger Wicker, R-Mississippi. "That is something that might speed the process along."

Sen. Ron Johnson, R-Wisconsin, also seems to like the idea, and he's also favors changing the rules to require 51 votes to limit debate on the Senate floor to just two hours on nominees.

"I think changing the rules to streamline the process in an appropriate way -- I mean, we should take a look at this," he said.

All three poured cold water on the idea of eliminating the filibuster for major legislation.

"There are going to be times when the Republicans are in the majority, and there are going to be times when we're in the minority," Wicker told CBS. "I still think there's a need for a body where consensus has to take place. If we hadn't had the 60-vote rule during the early days of President Obama, this would be a far different federal government. So I think we should tread very carefully when it deals with filibuster reform."

When Democrats still controlled the Senate, they invoked the nuclear option in November 2013 and eliminated the filibuster for most presidential nominations, except for the Supreme Court. It was the first major change in rules since 1975 when the Senate reduced the number of votes required for cloture, or ending debate, from two-thirds to three-fifths of the Senate, or 60 of 100 senators.

Given these developments, and the elimination of the filibuster for Supreme Court nominations earlier this year, some fear that the Senate is creeping toward the elimination of the filibuster for legislation.

"I've described it as a slippery slope," said Arenberg. "I suspect that we'll come to a day when a majority in the Senate will face an issue so important to their base that they'll be tempted to roll this precedent out and use it. I hope we don't get to that, but I do fear that."