The relationship between government expenditure and exchange rate is an important one. The key question in current policy and academic debates is What are the effects of fiscal policy on aggregate economic activity in a globalized world?
The central challenge in this debate is how to identify fiscal shocks in the data. Auerbach and Gorodnichenko (2015) address this challenge by using daily data on US government spending. Exploiting this high-frequency data, they find that unexpected government spending instantly affects exchange rates and the dollar appreciate, which if I understand correctly supports your intuition.
The direction of the response of the exchange rate is consistent with basic macroeconomic theory; in an economy with a flexible exchange rate, government spending shocks should lead to appreciation of the domestic currency.