NEW YORK (CNN/Money) - When Alan Greenspan testifies to Congress Tuesday, he may feel like a guy with two jealous girlfriends standing by to see whom he says he really loves.

The stock market wants to hear him declare his undying faith in the economic recovery, the one where the GDP's growth rate is supposed to double this quarter and next, according to the optimistic view on Wall Street. It needs to see its high price-to-earnings ratios validated, and the Fed chairman could definitely woo it with a rosy economic scenario.

The bond market wants to hear him worry about deflation, the possibility that the economy remains so soggy that inflation falls to zero and below. That would open the door to another rate cut or even the possibility of the Fed buying up notes and bonds at some point to thwart deflation, very bullish for bonds.

Greenspan, like anybody cocky enough to date two people at once and string both of them along, is no doubt confident he can pull this off. Hasn't he been sweet-talking both markets with his emphasis on high worker productivity? Strong productivity means that companies can produce a lot more goods and services with the same number of workers working the same number of hours.

And in a weak labor market like this one, there's not a lot of urgency for companies to grant fat raises. That's the basis for an economy that can grow at a much faster rate without creating a rising inflation rate. Better growth is what stocks want to hear. Low inflation and the implicit hint it contains that the Fed would tolerate much stronger growth before raising interest rates is what bonds want to hear.

Problem is the bond market is feeling a bit like a jilted lover right now and it may not succumb to Greenspan's obvious attempt to win it back.

Before the Fed's last meeting on June 25, Mr. G. spoke many times about the small but real risk of deflation. He has also mentioned on many occasions, as have other Fed officials, the Fed's readiness to adopt extraordinary measures to fight deflation should interest rate cuts start to lose their impact -- measures like the Fed buying up quantities of notes and bonds.

For the bond market, that's like saying "hey baby, what's your favorite shape of diamonds, because I'm about to go shopping for one." In the bond market it was taken as a signal the Fed was thinking very seriously about cutting its key short-term rate by a half-percentage point instead of opting for a more cautious quarter-point cut. Like a woman thinking she's about to get a shiny engagement ring, bonds rallied into the last meeting.

And then what happened? The Fed opted for the smaller rate cut. Not good for bond bulls looking for the Fed to go all the way. And it continued to issue a bifurcated policy statement. One where it said what stocks wanted to hear, that the chance of growth being too low or too high are now balanced, instead of saying the risk is balanced toward weakness as it did at its May 6 meeting. And one where it said what bonds wanted to hear, that the risk of an unwelcome drop in inflation -- that's the deflation hint -- was greater than the chance inflation would rise.

But it didn't work. Bonds started selling off and sold off for days. The yield on the U.S. Treasury 10-year note went from a low of 3.07 percent, achieved when the bond market thought Greenspan only had eyes for deflation and fixed-income, to a high of 3.7 percent on July 7th, the height of its fury.

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No matter what Greenspan says tomorrow it's going to be hard for him to get the bond market to give him another chance. And it will be especially difficult now that the stock market is doing what the Fed wants it to do -- it's rallying and that is supposed to help make businesses confident enough to start hiring again and start investing again, and it's also supposed to make investors who are also consumers feel better about spending some more money.

After all, even with the back-up in bond yields, 30-year fixed mortgage rates are still just around 5.5 percent and they aren't expected to go much above 5.7 percent. That's still plenty low for most homebuyers. Not too much of a sign yet that other kinds of consumer spending are really accelerating but, hey, the tax cuts are only just now starting to take effect and the weather has been nicer so maybe that's going to kick in now. Jobless claims are still too high, but if the virtuous cycle has really started that will fall into place, too.

Greenspan, gentleman that he is, no doubt will show that he still respects the bond market, even if their relationship has cooled off a bit. He is expected to say he agrees with Wall Street that growth can accelerate north of 3 percent in the second half, and also predict that core inflation stays well below 2 percent. If he really wants to win points, he'll go out of his way to indicate that it's fine with him if inflation goes higher, he won't raise interest rates until growth is back to potential (3.5 percent or higher).

Can he pull it off? Tomorrow at 10:00 eastern, we'll watch Sir Alan turn on the charm.  

Kathleen Hays anchors The FlipSide, airing Monday to Friday on CNNfn. As part of CNN's Business News team, she is also a regular contributor to Lou Dobbs Moneyline.