CLEVELAND (TheStreet) -- The city of Cleveland heads into the Republican National Convention with high hopes the event will boost the local economy, but the days leading up to the four-day GOP gathering left some underwhelmed.

The media buzz surrounding the convention has been enormous, with some projecting the RNC could bring Cleveland anywhere from $200 million to $400 million, but the environment here, thus far, has been relatively relaxed. Local business owners and residents wondered whether the huge extravaganza headlined by presumptive nominee Donald Trump would really bring in the influx of dollars promised.

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One driver for ride-sharing company Uber complained that business had been slow, criticizing the San Francisco-based company for bringing in drivers from Chicago, Philadelphia and other neighboring cities to help cart around the influx of people she said she hadn't yet witnessed. "We could have handled it," she said, noting that she was beginning to regret her decision to take off from her second job for the month of July.

Rival ride-sharing company Lyft has reportedly also recruited drivers from other areas.

Another woman working at a wine shop in Cleveland's Little Italy district said she, too, had yet to experience the anticipated boom in business. "Maybe it will pick up later in the week," I offered. She seemed unconvinced.

The Cleveland 2016 host committee has estimated that more than 50,000 people will descend on the city this week for the convention, though by the afternoon Sunday some were beginning to doubt whether that number might be a bit on the high side. Some residents said they had heard local caterers had been disappointed in the orders they received for planned gatherings and events.

Many notable Republicans have said they will be skipping the convention this year, including former Presidents George W. Bush and George H.W. Bush as well as Mitt Romney, John McCain and Lindsey Graham. Ohio Governor John Kasich will be in Cleveland this week, but he probably won't set foot in the Quicken Loans Arena, where the event will take place.

Despite a somewhat slow start, and some missing prominent GOPers, expectations remain that more attendees will arrive and business will pick up. Even Trump, the man of the hour, hadn't yet touched down in Cleveland over the weekend.

Some big corporate and media names have set up shop around the city. Twitter (TWTR) - Get Report has rented out Greenhouse Tavern, a restaurant in downtown Cleveland, for the week. CNN has done the same in downtown bar-restaurant Henry Buffalo. Politico has set up its own hub on the penthouse floor at the Former Huntington Building downtown.

Brands have set up shop inside and outside convention hall as well. Facebook (FB) - Get Report has a hub just outside the arena; FedEx (FDX) - Get Report has a tent outside Progressive Stadium; Microsoft (MSFT) - Get Report has displays set up for both Skype and its Surface products inside the arena.

How the Republican convention will really shake out will be seen in the days to come, with official activities kicking off here today at 1:00 p.m. But thus far, Cleveland seems relatively underwhelmed by the GOP extravaganza -- after all, the city did just host over a million people in town to celebrate the Cavaliers' NBA championship.

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