There are two possible procedures for proposing an amendment.
1. Both houses of the US Congress must pass a bill with a 2/3 vote in each house.
2. Constitutional convention. The legislatures of 2/3 of the states call on Congress to call a national convention to propose an amendment. This procedure has never been used.
Ratifying the proposed amendment also has two possible options.
1. The legislatures of 3/4 of the states ratify. Currently that would take 38 states.
2. The states call ratifying conventions to allow a more direct vote by the people of the state. This has only occurred once, with the repeal of prohibition (21st Amendment). Again, it takes 3/4 of the states to approve.
The US Supreme Court has stipulated that ratification must be completed within "some reasonable time after the proposal." There isn't a specified amount of time, but it has most often been set at 7 years.
The President of the United States plays no official role in this process. His signature is not required to either propose, ratify, or certify. (Some presidents have signed amendments as witnesses during the certification, but they were unnecessary).
That is the process. Now for the obstacles.
In the past, most amendments have been proposed and ratified because there was a broad consensus across all parties and ideologies as to the necessity of the particular amendment. Reasoned and civil discourse in our country has deteriorated to the point that it would be unrecognizable to those previous generations. The only time in our history that I see as being comparably polarized is during the Civil War era. Consensus will not be achieved, bipartisan support will not be given, for any amendment procedure that is even slightly ideological. And this is a paradox. The more that the ideologues seek purity in their parties, and purity in constitutional laws and doctrines, the more polarized the country becomes and the less likely that they will see their particular ideology given Constitutional fiat through amendment.
Could 2/3 of the states agree on an ideological amendment and call a convention? Take the Fair Tax. Are there 2/3 of the states that are conservative enough to want it? And what vein of conservatism do they value? Is it the Goldwater libertarian conservatism we see in several Western states? Or is it the type of conservatism embodied by Mike Huckabee's South in which social issues rule the day, to the point of espousing big government entitlement programs gussied up to look like Christian charity? If the South and the West can't even agree on their presidential nominees, how can they agree in a constitutional convention? Given the historical fact that this option has never been used, I would say that even in more civil times this option was unrealistic.
So that leaves us with the prospect of needing 67% of the House and 67% of the Senate to vote for an amendment. I was curious to see if the Republicans had ever had 67% of the Senate. This website breaks down the numbers of Senators from each party for every Congress. The 35th Congress (1857-59) was the first Congress for Republicans. From that time the years in which Republican had 67% or more of the Senate were: 1865-67 (72%), 1867-69 (83.8%), 1869-71 (83.8%), 1871-73 (75.7%). They just missed it in 1907-09 with 66.3%. The lowest they ever had was in 1937-39 at 16.7%.
In modern times (Reagan era forward) the best numbers they ever had were 55% in 83-85, 97-2001, and 05-07. So the surges with the Reagan and Gingrich revolutions fell well short of 67%. And the 2010 elections failed to even break 50%.
Note that the most controversial amendments ever passed, the 13th (prohibiting slavery), 14th (guarantees the rights of citizens), 15th (grants black men the right to vote) were all ratified between 1865-69. Years when the GOP had well over 67% of the Senate, and I presume, had overwhelming control of the state legislatures as well.
The 16th Amendment (income tax) was proposed in 1909, when the GOP had 66.3% of the Senate. Prohibition (18) and its repeal (21) were peculiar to their day, with populist support from both parties. Ensuring women the right to vote (19) was also a populist movement with broad support from both parties.
In modern times, at the height of the sexual revolution, the feminists were unable to get the Equal Rights Amendment passed. And at the height of the Gingrich revolution, the GOP couldn't get much traction with a less controversial Balanced Budget Amendment.
Will there ever be another ideological amendment passed again, such as the 13th, 14th, and 15th? I would say, barring another civil war, no. Absolutely no.
It is a dereliction, a shirking of the most profound magnitude, for our politicians to be wasting time and energy pushing for sure looser proposals, like the Fair Tax or the repeal of the 17th Amendment, when there are giant, looming problems threatening to destroy our nation. They hide behind the skirts of these silly, fairy tale proposals while America teeters on the brink.
From the FairTax Fairy website we read:
Do women have the right to vote in this country? Did we pass Prohibition? Did we repeal it? Do Civil Rights guarantee freedoms far beyond the lunch counter and mass transit? Do free-market economies dominate Eastern Europe, peoples once under the boot of communism? All these were grassroots efforts that effected significant changes in our nation and the world. Is the current income tax system any less a yoke around the necks of otherwise free peoples? We think not.
Passing the original 16th Amendment and the income tax wasn’t easy and repealing the income tax and the 16th Amendment won’t be easy either. That is why the FairTax has undertaken to build a grassroots movement and grassroots alliances to support the effort.
From their website, which hasn't been updated since the new Congress was sworn in, they list only 10 Senators supporting this tax. Meanwhile, the US marches towards insolvency and the proponents of this system fail to propose any real reform to taxes that have a chance of actually seeing the light of day.
Sources for Amendment procedure: 1 2
Source for Amendment dates.