Quoting matt_black's answer:
In fact you could probably drink it with few ill effects.
Indeed, as described here (link is to a PDF), there are documented cases where individuals consumed appreciable quantities of mercury metal and did not suffer dramatic long-term medical consequences (citation markers removed here and in all quotes below):
Herewith, it is useful to recall two rather bizarre examples of oral intake of liquid mercury, confirming that the risk of acute poisoning is indeed minimal. First, it is a story of unlucky love in the former Czechoslovakia, when a desperate girl voluntarily swallowed several grams of mercury. Instead of the expected death, she had recovered soon and, since then, became the wanted object of exhibition at medical faculties for several years, when the students and other university staff could observe under a roentgen irradiation how the mercury circulated in her blood system, including its passage through the pumping heart. The second case is then a criminalistic legend from the old Austro-Hungarian Empire, when a (never-revealed) joker had injected liquid mercury into bonbons that were subsequently distributed among the VIPs attending the famous ball at Vienna's Opera. According to the contemporary press, almost every infected victim had suffered from a strong diarrhea (almost demolishing the toilets), but no-one died or being otherwise seriously endangered.
The above PDF link also corroborates matt_black's and Brace's arguments about the primary mechanism of toxicity deriving from the vapor, not the liquid, of elemental mercury:
Inhalation of $\ce{Hg}$-vapors by lungs is practically complete. The acute inhalation of high concentrations of metallic $\ce{Hg}$-vapors may cause severe chemical pneumonitis and noncardiogenic pulmonary edema.
Chronic intoxication from inhalation of mercury vapor produces a classic triad of tremor, neuropsychiatric disturbances, and gingivostomatitis.
Due to high solubility in fats, $\ce{Hg}$-vapors come into brain circulation in few minutes. They cross hematoencephalic barrier, acting neurotoxically. It is expected that, in brain tissue, elemental mercury is oxidized to $\ce{Hg^{II}}$ and these species cross the hematoencephalic barrier being then accumulated in cortex and basal ganglions. Similarly, mercury can be transformed by catalase to $\ce{Hg^{II}}$ in erythrocytes and this divalent form is then distributed into tissues, interacting readily with the $\ce{–SH}$ groups in the enzymes. The highest depot is present in kidneys; usually, in adrenals. The kidneys tissue reacts by producing metallothioneins (MTs; cysteine-rich proteins) which effectively bind mercury. As a consequence, kidney-namely: proximal tubulus and glomerulus-are badly damaged after such saturation.
The Wikipedia page on mercury poisoning linked to by Phillipp in a comment to the question does also have some further elaboration of the topic:
Quicksilver (liquid metallic mercury) is poorly absorbed by ingestion and skin contact. Its vapor is the most hazardous form. Animal data indicate less than $0.01\%$ of ingested mercury is absorbed through the intact gastrointestinal tract, though it may not be true for individuals suffering from ileus. Cases of systemic toxicity from accidental swallowing are rare, and attempted suicide via intravenous injection does not appear to result in systemic toxicity, though it still causes damage by physically blocking blood vessels both at the site of injection and the lungs. Though not studied quantitatively, the physical properties of liquid elemental mercury limit its absorption through intact skin and in light of its very low absorption rate from the gastrointestinal tract, skin absorption would not be high. Some mercury vapor is absorbed dermally, but uptake by this route is only about $1\%$ of that by inhalation.