According to Orlando Figes in A People's Tragedy (I recommend), the Bolshevik coup was not a mass of people charging the Winter Palace. Lenin's version of Communism was not that Communists would take over the country in mass risings- that it would instead be undertaken by a "vanguard" of committed revolutionaries. The Bolsheviks themselves did not have mass support (when the Constituent Assembly was convened in 1918 out of 41 million votes cast, the Bolsheviks got 9 million). Their main supporters were the workers in the cities, and there were very few of them. The Bolsheviks distrusted Peasants especially, who made up the vast majority (80%) of the population. The Bolsheviks had amassed most of their strength following the Kornilov affair in August 1917, when Kerensky (leader of the Provisional Government) had released and armed the Bolshevik prisoners in the jails. This gave the Bolsheviks leverage to say they were defending the revolution and as a result their percentage of the vote in the Soviets increased massively. The overthrow of the Provisional Government (which had taken over from the Tsar in the February Revolution) took place in Petrograd on the 5th of November. Lenin used his Red Guards (a worker's militia) to take over all of the most important parts of the town, including railway stations, waterworks, electrical stations etc. Soon only the Winter Palace needed to be taken. And it was taken, because it was defended only by some Cossacks, military students and a women's battalion, most of whom went home anyway because they got hungry or homesick before the final assault by the Bolsheviks came. Indeed, the Provisional Government was captured by a small group of Bolsheviks who broke in and got lost, and then just accidentally ran into the Provisional Government. There were similar such uprisings and capturing of the main urban centres around Greater Russia. The Bolsheviks enforced their control through control of the Soviets, which were the groupings of proletarian representatives elected by the workers and soldiers. The Bolsheviks had long supported "All power to the Soviets", and had a large amount of representatives there because the Soviets were elected by the urban proletarians. The Social Revolutionaries (another socialist political party) had split into Left and Right in November. The Bolsheviks formed a coalition with the Left Social Revolutionaries. On January the 14th of 1918, the Mensheviks and moderates in the Soviets walked out in protest at the Second All Russian Congress of Soviets, allowing the Bolsheviks and Left SRs to ratify the transfer of power from the Provisional Government to the Soviets because they were the only ones left in the Soviet, allowing them to pass whatever laws and decrees they wanted. On the 19th of January, the elected Constituent Assembly was dissolved by the Soviets, and the Bolshevik political takeover of urban Russia was complete. Roll on the civil war. In regard of your question, it was not a mass uprising that overthrew the Provisional Government. It was more a question of the Provisional Government becoming so weak that it posed no threat to the small, professional groups of Red Guards which Lenin released upon Petrograd. Although there were Peasant uprisings, these were unconnected to the Bolshevik seizure of power (The peasants liked to take over land whenever they smelt trouble). Kerensky's governmental weakness was based mainly on the fact that it was made by the urban liberals- the Soviets were more democratic insofar that they were elected by the mass of the urban population. Even then, the Bolsheviks were not much of a leading party and they were the only party that supported a military takeover of the Provisional Government.

It seems to me the answer of the question is yes and no. Clearly the Bolsheviks were not the most popular party and most people point to the election results of late 1918 as evidence. The SRs remained the most popular party, although the Bolsheviks received the second most votes. But mass support has different dimensions than whether a party in a given election has to most votes. I find the 'coup' narrative rather unpersuasive, and instead think it more likely that it is a product of an ideological culture that viewed the later USSR as the epicenter of evil. From this point of view, such a pernicious political formation could only be the product of a vile conspiracy launched by cynical, manipulative politicians against the will of the country's population.

I think the evidence points to a more complicated scenario. For one, only Lenin among top Bolsheviks in April-June of 1917 advocated for a second revolution against the Provisional Government. Rather, it was the huge influx of new party members in the mid and late summer of 1917 who demanded a more radical response from the party and to whom the party listened. Most of the new delegates at the sixth congress in July 1917 were new members who joined in 1917, and 94% were new since 1914. These people pressed for a more radical shift in power to the soviets and the leading Bolsheviks listened.

Others would also point to the fact that during the Civil War, the Bolsheviks employed the Cheka to repress both legitimate counter-revolutionaries, and non-Bolshevik socialist dissenters, many of whom were peasants. But it is perhaps worth pointing out that most peasant resistance did not begin with October, nor even with the dissolution of the Constituent Assembly in January 1918. After all, the Bolsheviks immediately ratified the peasants' own revolution in the countryside once they came into power. Peasant resistance became most acute during the Civil War when the Bolsheviks turned to old tsarist tactics for organizing, arming, and feeding an army - 'grain requisition,' the sterile moniker for sending cadres into villages to confiscate produce.

I think these factors depict the Bolsheviks as being led perhaps by pragmatic revolutionaries who are willing to go to great lengths to defend their revolution (or, in more cynical terms, to defend their power), but the party also swelled with and responded to the demands of the idealistic popular movement. Many historians think Lenin was part of that idealism as well, despite his willingness to use state violence for political ends. At the very least, it seems clear that a measured look at the revolution shows that the Bolsheviks were not merely cynical politicians manipulating popular opinion to construct a totalitarian state. Even still, I think that explanation is entirely wrong.

In terms of international support, there was a fair amount of aid sent to the White Russians by the United States and the US even sent troops to fight in Archangel against the Bolsheviks in 1918.

Edit: Grammar