What you say makes no sense. If a company ships jobs overseas, they avoid very little tax. Example: Take a printer made by Company A in the US and sold in the US. Company A decides to outsource the printer making jobs to Malaysia, and then re-import and sell the printers in their US market. TCompany A is still liable for the state and federal corporate taxes on its profits. The purchaser is still liable for the sales tax. The only tax savings for Company A is the payroll tax for the employees it no longer has in the US. If that was sufficient incentive to outsource, it would have happened in 1935, when the social security tax was first implemented. It would have accelerated in 1965, when Medicare as added to the payroll tax. It would have accelerated even more in the 1980's, when social security taxes were increased. None of that happened because payroll tax avoidance is not a sufficient reason to outsource.
The advantage came in the 90's, when the worldwide boom in capitalism after the fall of the Soviet Union allowed emerging economies to develop sufficient infrastructure to handle the shipping of raw goods in and finished goods out. Emerging economies also developed semi-skilled labor that was still very cheap. At that point, outsourcing made sense. Which liberal policy was it that caused the fall of the Soviet Union? None. Reagan did that, as any good conservative will tell you. After that, it was just good old fashioned capitalism and free enterprise that led to economic boom times in emerging economies. Which liberal do you want to credit for that? Companies outsourced jobs when it became profitable for them to do so, not because they wanted to save a few bucks on payroll taxes.
Another reason companies outsource jobs now is that overseas economies are increasingly profitable places to sell goods. That's where tax policy kicks in. A US company that produces a product in Country X and sells that product there is not taxed on the profit of that transaction in the US. That's right. Companies can avoid state and federal corporate taxes by outsourcing jobs to locations that serve as foreign markets for their products. Now, which liberal do you suppose advocated that tax policy? None. In fact, one of Obama's campaign issue was to tax such profits.
Now, I'm not going to turn the tables and blame outsourcing on conservatives. Free trade and global capitalism are good things in general, but they quite naturally lead to increased outsourcing from developed countries with higher labor rates to less developed countries with lower labor rate. Unless you want to give liberals credit for free trade and global capitalism, don't blame liberals for outsourcing.