Biochemist Dr. Fazale Rana of Reasons to Believe offers some evidence.

Excerpt:

Today, the Miller-Urey experiment is considered to be irrelevant to the origin-of-life question. Current understanding of the composition of early Earth’s atmosphere differs significantly from the gas mix used by Miller. Most planetary scientists now think that the Earth’s primeval atmosphere consisted of carbon dioxide, nitrogen, and water vapor. Laboratory experiments indicate that this gas mixture is incapable of yielding organic materials in Miller-Urey-type experiments.

In May 2003 origin-of-life researchers Jeffrey Bada and Antonio Lazcano, long-time associates of Miller, wrote an essay for Science (May 2, 2003, pp. 745-746)commemorating the 50-year anniversary of the publication of Miller’s initial results.They pointed out that the Miller-Urey experiment has historical significance, but not scientific importance in contemporary origin-of-life thought. Bada and Lazcano wrote:

Is the “prebiotic soup” theory a reasonable explanation for the emergence of life? Contemporary geoscientists tend to doubt that the primitive atmosphere had the highly reducing composition used by Miller in 1953.

In his book Biogenesis, origin-of-life researcher Noam Lahav passes similar judgment:

The prebiotic conditions assumed by Miller and Urey were essentially those of a reducing atmosphere. Under slightly reducing conditions, the Miller-Urey reaction does not produce amino acids, nor does it produce the chemicals that may serve as the predecessors of other important biopolymer building blocks. Thus, by challenging the assumption of a reducing atmosphere, we challenge the very existence of the “prebiotic soup”, with its richness of biologically important organic compounds.

For many people, the generation of amino acids from simple chemical compounds thought to be present in early Earth’s atmosphere meant that life could originate all on its own without the need for a Creator. Work done on the early planetary conditions of Earth in the intervening decades between Miller’s famous experiment and his death, however, have invalidated this famous experiment and its support for an evolutionary explanation for life’s origin, in spite of what textbooks report.

The IDEA Center has a nice summary of origin-of-life research that explains why scientists no longer accept the idea that the building blocks of life can be formed by sparking the gasses that were present on the early Earth.

Miler and Urey used the wrong gasses:

Miller’s experiment requires a reducing methane and ammonia atmosphere, however geochemical evidence says the atmosphere was hydrogen, water, and carbon dioxide (non-reducing). The only amino acid produced in a such an atmosphere is glycine (and only when the hydrogen content is unreasonably high), and could not form the necessary building blocks of life.

Miller and Urey didn’t account for UV of molecular instability:

Not only would UV radiation destroy any molecules that were made, but their own short lifespans would also greatly limit their numbers. For example, at 100ºC (boiling point of water), the half lives of the nucleic acids Adenine and Guanine are 1 year, uracil is 12 years, and cytozine is 19 days (nucleic acids and other important proteins such as chlorophyll and hemoglobin have never been synthesized in origin-of-life type experiments).

Miller and Urey didn’t account for molecular oxygen:

We all have know ozone in the upper atmosphere protects life from harmful UV radiation. However, ozone is composed of oxygen which is the very gas that Stanley Miller-type experiments avoided, for it prevents the synthesis of organic molecules like the ones obtained from the experiments! Pre-biotic synthesis is in a “damned if you do, damned if you don’t” scenario. The chemistry does not work if there is oxygen because the atmosphere would be non-reducing, but if there is no UV-light-blocking oxygen (i.e. ozone – O₃) in the atmosphere, the amino acids would be quickly destroyed by extremely high amounts of UV light (which would have been 100 times stronger than today on the early earth).This radiation could destroy methane within a few tens of years, and atmospheric ammonia within 30,000 years.

And there were three other problems too:

At best the processes would likely create a dilute “thin soup,” destroyed by meteorite impacts every 10 million years. This severely limits the time available to create pre-biotic chemicals and allow for the OOL.

Chemically speaking, life uses only “left-handed” (“L”) amino acids and “right-handed” (“R)” genetic molecules. This is called “chirality,” and any account of the origin of life must somehow explain the origin of chirality. Nearly all chemical reactions produce “racemic” mixtures–mixtures with products that are 50% L and 50% R.

Two more problems are not mentioned in the article. A non-peptide bond anywhere in the chain will ruin the chain. You need around 200 amino acids to make a protein. If any of the bonds is not a peptide bond, the chain will not work in a living system. Additionally, the article does not mention the need for the experimenter to intervene in order to prevent interfering cross-reactions that would prevent the amino acids from forming. That’s another problem with the origin of life – experiments show that getting the building blocks requires an intelligence to intervene.

Now keep in mind that even if you get the building blocks, you are left with the sequencing problem – but that’s another topic for another day.