There are limits, yes. They are not nearly as restrictive as some would like, but they are there.

First, and most obviously, the government can't do anything that's expressly prohibited. For example, it cannot impart titles of nobility. It can't waive the writ of habeas corpus except in extreme cases. (It was done during the American Civil War, but never before or since then.) It can't impose a state religion, or interfere with free speech or a free press. And so it can't spend money towards any of these ends.

Secondly, the spending of money must be to promote the common defense and the general welfare of the United States -- that is, the defense or welfare of all of the states, all of the people; the government is not allowed to play favorites. (There are some things done by the federal government that might arguably violate this restriction, actually. In my opinion. Don't know whether it's been tested in court.)

Third, the power to spend money is ONLY the power to spend money; it's not the power to legislate by the back door. This came out in the Supreme Court case U.S. v. Butler, in which the Agricultural Adjustment Act was found unconstitutional. The AAA's goal was to regulate agricultural production so as to prop up prices. To do this, the government wanted to get farmers to stop producing so much, to leave some fields fallow. Now the federal government actually has no authority to regulate agricultural production directly; it can regulate the interstate sale or transportation of farm produce, but not production on the farm itself. (The state governments DO have this authority.) What the AAA did, was to levy a tax on food processing plants -- which in itself was constitutional -- and then use the revenue from that tax to provide subsidies to farmers who agreed voluntarily to abide by the restrictions the government imposed. The court ruled that this use of federal spending and taxation amounted to the enforcement of a regulation which the government had no authority to impose, and so was an unconstitutional use of the taxation/spending power.

Today, we have a different system of farm subsidies, which are not tied to attempts to regulate farm production, and so would pass that test (although not IMO the test of common sense -- but that's off-topic). There may be some other things the fed does in the way of conditional grants to the states that might violate the Butler ruling; I'm sure these have been tested in court, but I don't know what arguments allowed them. It's not the method of conditioned spending per se that the Butler decision voided, but rather its use to impose a non-authorized regulation by the back door.