"This is the first clear indication that Europe is starting to be aggressive again," Tchir said. "There could be some volatility in bonds as people decide how good or bad it is, but I think the net decision will be that it is good."
The rescue money will come from pools set up by other euro countries. Spain's government will distribute it to the banks. The banks will pay it back with interest, and the money will go back to the rescue pools. Interest rates and other details had not been revealed Sunday.
By shifting some of the risk to other countries, Spain buys time to sort out its crisis. And European leaders have an opportunity to roll out more confidence-building measures.
Tchir said he drew hope from the international coordination that led to the Spanish bank bailout. He noted that the International Monetary Fund was involved, without having given any money.
And U.S. Treasury Secretary Timothy Geithner issued a public statement quickly after the news from Spain, signaling strong coordination among U.S. and European leaders.
"Europe realized they were on the cusp," Tchir said. "I think (world leaders) decided, 'Let's figure out a bunch of things that give us a big push and another six months to get our economies in order."
For that to happen, he said, Europe will have to encourage economic growth by backing off demands for massive spending cuts by Greece, Portugal and Ireland, the three nations that have already received bailouts in exchange for agreeing to deep and painful cuts.
Greece holds an election next Sunday, and the leader of Syriza, a far-left Greek political party, has vowed to cancel Greece's international bailout agreement if the party wins.
That could ultimately lead to Greece's exit from the euro, further inflaming the crisis, and could wipe out any gains that U.S. stocks and other investments enjoy after the Spanish bank bailout.
U.S. investors are already worried about slowing job growth at home, and a prolonged crisis in Europe only adds to the challenge for the U.S. economy by hurting the market for U.S. exports.
"We have a lot of political, economic and fundamental headwinds that are not simply going to be dealt with by offering some money to bail out Spanish banks," Stovall said.
He said there are plenty of reasons to expect a rally that could last for a couple of weeks without eclipsing the market's recent high.
That was April 2, when the S&P closed at its highest level since the financial crisis of 2008. The Dow's post-crisis high was May 1. The S&P is down 6.6 percent from that high and the Dow 5.5 percent, largely because of fear about Europe.
Stovall said investors should view any stock bounce this week in a long-term context. The bailouts might lift U.S. stocks for a few days, he said, but "I don't feel confident enough to say that it would also support a long-term rally."
Daniel Wagner can be reached at www.twitter.com/wagnerreports.