Today tariffs average a mere 1.3% , which is quite low by historical levels, where tariffs have more typically been in the 10%-30% range. What would be the effect of raising the average tariff to 10%? The US imported $2299B of goods and services in 2012 , and exports of $1564B in the same year , so we'll use these number for a simple analysis.
What effect would that 10% tariff have on the balance of trade? This is a complicated question but one for which we can make some simple estimates. A recent study of the effects of trade barriers  finds that "The elasticity of imports to the domestic cost of importing is about
0.50, and that of exports to the domestic cost of exporting is about
0.48. That is, a 10% reduction in the cost associated with importing
(exporting) would increase imports (exports) by about 5% (4.8%)." Per country details vary but we can nonetheless use these values to estimate the effect of changes in tariffs on the level of imports and exports for the US. An increase in tariffs acts the same way. That is, for imports an increase in the tariff of 10% will decrease the amount of imports by 5%. A tariff is just a percentage increase in price of an imported good.
Elasticity is a bit difficult for many people to understand. But it basically says if I perturb one value a little bit, how much does the other value change? In the case of imports a small change in price causes half as much change in imports. A key concept here is that elasticity is only valid for small changes in values. Even the change of 10% in price is probably a bit unrealistic, but it will nonetheless give us some idea of how imports are changing with price.
Balancing trade requires that the level of imports equals the level of exports. So, to decrease the level of imports to that of the level of exports in 2012 is a drop from $2299B to $1564B, which is a large reduction of imports of 32%. Given the elasticity factor of tariffs for imports of 0.50, this means the tariff increase needed on imports to achieve this goal is 32%/0.50 = 64%. This is a large tariff by historical standards, and in practice this amount may not be needed as the actual adjusting of trade is not so simply defined by the elasticity.
The complexities of trade suggest that an incremental approach to tariff be taken. Start by increasing the tariff to 10% one year and see the effects. Perhaps increase the tariff again the next year and see the effects. Continue increasing the tariff until trade comes to a balance. Or in the case of the US, a surplus is generated, which is needed to pay down the years of accumulated trade deficits.
A second benefit of the tariff is raising revenue for the government. A simple application of the tariff assuming no change in imports for a
10% tariff to all of the new level of imports of $2184B it would produce $218.4B of
revenue for the US government, which is $190B more than the government
collected would have collected. Tariffs reduce the tax burden on Americans and
helps balance the budget as well as affecting trade.
Still using general references due to the government shutdown
 Hoekman, Bernard & Nicita, Alessandro, 2011.
"Trade Policy, Trade Costs, and Developing Country Trade,"
Elsevier, vol. 39(12), pages 2069-2079.